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Journal articles on the topic 'Non-abelian tensor product'

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Published: 9 March 2023

Last updated: 10 March 2023

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1

Moghaddam, Mohammad Reza R., and Fateme Mirzaei. "On the Non-abelian Tensor Product of Groups." Algebra Colloquium 18, no. 03 (September 2011): 429–36. http://dx.doi.org/10.1142/s1005386711000319.

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In this paper, we study some properties of the non-abelian tensor product of two groups G and H. More precisely, if G is abelian and H is a nilpotent group, then an upper bound for the exponent of G ⊗ H is obtained. Using our results, we obtain some upper bounds for the exponent of the Schur multiplier of the non-abelian tensor product of groups. Finally, an abelian group is constructed by taking non-abelian tensor product of groups.

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2

Castiglioni, J. L., X. García-Martínez, and M. Ladra. "Universal central extensions of Lie–Rinehart algebras." Journal of Algebra and Its Applications 17, no. 07 (June 13, 2018): 1850134. http://dx.doi.org/10.1142/s0219498818501347.

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In this paper, we study the universal central extension of a Lie–Rinehart algebra and we give a description of it. Then we study the lifting of automorphisms and derivations to central extensions. We also give a definition of a non-abelian tensor product in Lie–Rinehart algebras based on the construction of Ellis of non-abelian tensor product of Lie algebras. We relate this non-abelian tensor product to the universal central extension.

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3

THOMAS, VIJI Z. "THE NON-ABELIAN TENSOR PRODUCT OF FINITE GROUPS IS FINITE: A HOMOLOGY-FREE PROOF." Glasgow Mathematical Journal 52, no. 3 (August 25, 2010): 473–77. http://dx.doi.org/10.1017/s0017089510000352.

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AbstractIn this note, we give a homology-free proof that the non-abelian tensor product of two finite groups is finite. In addition, we provide an explicit proof that the non-abelian tensor product of two finite p-groups is a finite p-group.

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4

Ellis, Graham J. "A non-abelian tensor product of Lie algebras." Glasgow Mathematical Journal 33, no. 1 (January 1991): 101–20. http://dx.doi.org/10.1017/s0017089500008107.

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A generalized tensor product of groups was introduced by R. Brown and J.-L. Loday [6], and has led to a substantial algebraic theory contained essentially in the following papers: [6, 7, 1, 5, 11, 12, 13, 14, 18, 19, 20, 23, 24] ([9, 27, 28] also contain results related to the theory, but are independent of Brown and Loday's work). It is clear that one should be able to develop an analogous theory of tensor products for other algebraic structures such as Lie algebras or commutative algebras. However to do so, many non-obvious algebraic identities need to be verified, and various topological proofs (which exist only in the group case) have to be replaced by purely algebraic ones. The work involved is sufficiently non-trivial to make it interesting.

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5

Gnedbaye, Allahtan Victor. "A non-abelian tensor product of Leibniz algebra." Annales de l’institut Fourier 49, no. 4 (1999): 1149–77. http://dx.doi.org/10.5802/aif.1712.

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6

Bastos, R., and N. R. Rocco. "Non-abelian tensor product of residually finite groups." São Paulo Journal of Mathematical Sciences 11, no. 2 (August 18, 2017): 361–69. http://dx.doi.org/10.1007/s40863-017-0069-5.

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7

Blyth, Russell D., Robert Fitzgerald Morse, and Joanne L. Redden. "ON COMPUTING THE NON-ABELIAN TENSOR SQUARES OF THE FREE 2-ENGEL GROUPS." Proceedings of the Edinburgh Mathematical Society 47, no. 2 (June 2004): 305–23. http://dx.doi.org/10.1017/s0013091502000998.

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AbstractIn this paper we compute the non-abelian tensor square for the free 2-Engel group of rank $n>3$. The non-abelian tensor square for this group is a direct product of a free abelian group and a nilpotent group of class 2 whose derived subgroup has exponent 3. We also compute the non-abelian tensor square for one of the group’s finite homomorphic images, namely, the Burnside group of rank $n$ and exponent 3.AMS 2000 Mathematics subject classification: Primary 20F05; 20F45. Secondary 20F18

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8

Gilbert, N. D., and P. J. Higgins. "The non-abelian tensor product of groups and related constructions." Glasgow Mathematical Journal 31, no. 1 (January 1989): 17–29. http://dx.doi.org/10.1017/s0017089500007515.

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The tensor product of two arbitrary groups acting on each other was introduced by R. Brown and J.-L. Loday in [5, 6]. It arose from consideration of the pushout of crossed squares in connection with applications of a van Kampen theorem for crossed squares. Special cases of the product had previously been studied by A. S.-T. Lue [10] and R. K. Dennis [7]. The tensor product of crossed complexes was introduced by R. Brown and the second author [3] in connection with the fundamental crossed complex π(X) of a filtered space X, which also satisfies a van Kampen theorem. This tensor product provides an algebraic description of the crossed complex π(X ⊗ Y) and gives a symmetric monoidal closed structure to the category of crossed complexes (over groupoids). Both constructions involve non-abelian bilinearity conditions which are versions of standard identities between group commutators. Since any group can be viewed as a crossed complex of rank 1, a close relationship might be expected between the two products. One purpose of this paper is to display the direct connections that exist between them and to clarify their differences.

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9

Salemkar, Ali Reza, Hamid Tavallaee, Hamid Mohammadzadeh, and Behrouz Edalatzadeh. "On the non-abelian tensor product of Lie algebras." Linear and Multilinear Algebra 58, no. 3 (April 2010): 333–41. http://dx.doi.org/10.1080/03081080802590834.

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10

Casas, J. M., E. Khmaladze, and N. Pacheco Rego. "A non-abelian Hom-Leibniz tensor product and applications." Linear and Multilinear Algebra 66, no. 6 (June 21, 2017): 1133–52. http://dx.doi.org/10.1080/03081087.2017.1338651.

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11

García-Martínez, Xabier, Emzar Khmaladze, and Manuel Ladra. "Non-abelian tensor product and homology of Lie superalgebras." Journal of Algebra 440 (October 2015): 464–88. http://dx.doi.org/10.1016/j.jalgebra.2015.05.027.

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12

Casas, J. M., E. Khmaladze, and N. Pacheco Rego. "A Non-abelian Tensor Product of Hom–Lie Algebras." Bulletin of the Malaysian Mathematical Sciences Society 40, no. 3 (March 30, 2016): 1035–54. http://dx.doi.org/10.1007/s40840-016-0352-0.

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13

Beuerle, James R., and Luise-Charlotte Kappe. "Infinite metacyclic groups and their non-abelian tensor squares." Proceedings of the Edinburgh Mathematical Society 43, no. 3 (October 2000): 651–62. http://dx.doi.org/10.1017/s0013091500021258.

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AbstractIn this paper we classify all infinite metacyclic groups up to isomorphism and determine their non-abelian tensor squares. As an application we compute various other functors, among them are the exterior square, the symmetric product, and the second homology group for these groups. We show that an infinite non-abelian metacyclic group is capable if and only if it is isomorphic to the infinite dihedral group

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14

Bastos, R., I. N. Nakaoka, and N. R. Rocco. "Finiteness conditions for the non-abelian tensor product of groups." Monatshefte für Mathematik 187, no. 4 (December 9, 2017): 603–15. http://dx.doi.org/10.1007/s00605-017-1143-x.

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15

Ellis, Graham J. "The non-abelian tensor product of finite groups is finite." Journal of Algebra 111, no. 1 (November 1987): 203–5. http://dx.doi.org/10.1016/0021-8693(87)90249-3.

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16

Donadze, G., M. Ladra, and V. Z. Thomas. "On some closure properties of the non-abelian tensor product." Journal of Algebra 472 (February 2017): 399–413. http://dx.doi.org/10.1016/j.jalgebra.2016.10.045.

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17

Salemkar, Alireza, and Tahereh Fakhr Taha. "The non-abelian tensor product of normal crossed submodules of groups." Categories and General Algebraic Structures with Application 13, no. 1 (October 1, 2020): 23–44. http://dx.doi.org/10.29252/cgasa.13.1.23.

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18

Edalatzadeh, Behrouz. "A non-abelian tensor product of precrossed modules in lie algebras." Communications in Algebra 48, no. 4 (November 21, 2019): 1591–600. http://dx.doi.org/10.1080/00927872.2019.1691576.

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19

Gilbert, N. D. "The non-abelian tensor square of a free product of groups." Archiv der Mathematik 48, no. 5 (May 1987): 369–75. http://dx.doi.org/10.1007/bf01189628.

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20

Bastos, Raimundo, Noraí R. Rocco, and Ewerton R. Vieira. "Finiteness of homotopy groups related to the non-abelian tensor product." Annali di Matematica Pura ed Applicata (1923 -) 198, no. 6 (April 22, 2019): 2081–91. http://dx.doi.org/10.1007/s10231-019-00855-8.

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21

Hosseini, Seyedeh Narges, Behrouz Edalatzadeh, and Ali Reza Salemkar. "The non-abelian tensor product and the second homology of Leibniz algebras." Communications in Algebra 48, no. 2 (September 8, 2019): 759–70. http://dx.doi.org/10.1080/00927872.2019.1659288.

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22

Donadze, G., M. Ladra, and P. Páez-Guillán. "Schur's theorem and its relation to the closure properties of the non-abelian tensor product." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 150, no. 2 (January 26, 2019): 993–1002. http://dx.doi.org/10.1017/prm.2018.150.

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AbstractWe show that the Schur multiplier of a Noetherian group need not be finitely generated. We prove that the non-abelian tensor product of a polycyclic (resp. polycyclic-by-finite) group and a Noetherian group is a polycyclic (resp. polycyclic-by-finite) group. We also prove new versions of Schur's theorem.

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23

Mandal, Ashis, and Satyendra Kumar Mishra. "Universal central extensions and non-abelian tensor product of hom-Lie–Rinehart algebras." Colloquium Mathematicum 166, no. 1 (2021): 23–52. http://dx.doi.org/10.4064/cm8287-7-2020.

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24

Casas, J. M. "A non-abelian tensor product and universal central extension of Leibniz $n$-algebra." Bulletin of the Belgian Mathematical Society - Simon Stevin 11, no. 2 (June 2004): 259–70. http://dx.doi.org/10.36045/bbms/1086969316.

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25

di Micco, Davide, and Tim Van der Linden. "Universal Central Extensions of Internal Crossed Modules via the Non-abelian Tensor Product." Applied Categorical Structures 28, no. 5 (March 2, 2020): 717–48. http://dx.doi.org/10.1007/s10485-020-09595-w.

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26

Mohammed Khalid Shahoodh. "The Adjacency Matrix of The Compatible Action Graph for Finite Cyclic Groups of p-Power Order." Tikrit Journal of Pure Science 26, no. 1 (December 3, 2022): 123–27. http://dx.doi.org/10.25130/tjps.v26i1.109.

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Let G and H be two finites -groups, then is the non-abelian tensor product of G and H. In this paper, the compatible action graph for has been considered when and for the two finite -groups by determining the adjacency matrix for and studied some of its properties.

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27

Casas, J. M., and M. Ladra. "Non-abelian Tensor Product of Leibniz Algebras and an Exact Sequence in Leibniz Homology." Communications in Algebra 31, no. 9 (January 9, 2003): 4639–46. http://dx.doi.org/10.1081/agb-120022813.

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28

Dally, Malak M., and Mohammad N. Abdulrahim. "On the Unitary Representations of the Braid Group B6." Mathematics 7, no. 11 (November 9, 2019): 1080. http://dx.doi.org/10.3390/math7111080.

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We consider a non-abelian leakage-free qudit system that consists of two qubits each composed of three anyons. For this system, we need to have a non-abelian four dimensional unitary representation of the braid group B 6 to obtain a totally leakage-free braiding. The obtained representation is denoted by ρ . We first prove that ρ is irreducible. Next, we find the points y ∈ C * at which the representation ρ is equivalent to the tensor product of a one dimensional representation χ ( y ) and μ ^ 6 ( ± i ) , an irreducible four dimensional representation of the braid group B 6 . The representation μ ^ 6 ( ± i ) was constructed by E. Formanek to classify the irreducible representations of the braid group B n of low degree. Finally, we prove that the representation χ ( y ) ⊗ μ ^ 6 ( ± i ) is a unitary relative to a hermitian positive definite matrix.

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29

Duplij, Steven. "Graded Medial n-Ary Algebras and Polyadic Tensor Categories." Symmetry 13, no. 6 (June 9, 2021): 1038. http://dx.doi.org/10.3390/sym13061038.

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Algebraic structures in which the property of commutativity is substituted by the mediality property are introduced. We consider (associative) graded algebras and instead of almost commutativity (generalized commutativity or ε-commutativity), we introduce almost mediality (“commutativity-to-mediality” ansatz). Higher graded twisted products and “deforming” brackets (being the medial analog of Lie brackets) are defined. Toyoda’s theorem which connects (universal) medial algebras with abelian algebras is proven for the almost medial graded algebras introduced here. In a similar way we generalize tensor categories and braided tensor categories. A polyadic (non-strict) tensor category has an n-ary tensor product as an additional multiplication with n−1 associators of the arity 2n−1 satisfying a n2+1-gon relation, which is a polyadic analog of the pentagon axiom. Polyadic monoidal categories may contain several unit objects, and it is also possible that all objects are units. A new kind of polyadic categories (called groupal) is defined: they are close to monoidal categories but may not contain units: instead the querfunctor and (natural) functorial isomorphisms, the quertors, are considered (by analogy with the querelements in n-ary groups). The arity-nonreducible n-ary braiding is introduced and the equation for it is derived, which for n=2 coincides with the Yang–Baxter equation. Then, analogously to the first part of the paper, we introduce “medialing” instead of braiding and construct “medialed” polyadic tensor categories.

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30

BARNES, DAVID. "A monoidal algebraic model for rational SO(2)-spectra." Mathematical Proceedings of the Cambridge Philosophical Society 161, no. 1 (April 11, 2016): 167–92. http://dx.doi.org/10.1017/s0305004116000219.

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AbstractThe category of rational SO(2)–equivariant spectra admits an algebraic model. That is, there is an abelian category ${\mathcal A}$(SO(2)) whose derived category is equivalent to the homotopy category of rational SO(2)–equivariant spectra. An important question is: does this algebraic model capture the smash product of spectra?The category ${\mathcal A}$(SO(2)) is known as Greenlees' standard model, it is an abelian category that has no projective objects and is constructed from modules over a non–Noetherian ring. As a consequence, the standard techniques for constructing a monoidal model structure cannot be applied. In this paper a monoidal model structure on ${\mathcal A}$(SO(2)) is constructed and the derived tensor product on the homotopy category is shown to be compatible with the smash product of spectra. The method used is related to techniques developed by the author in earlier joint work with Roitzheim. That work constructed a monoidal model structure on Franke's exotic model for the K(p)–local stable homotopy category.A monoidal Quillen equivalence to a simpler monoidal model category R•-mod that has explicit generating sets is also given. Having monoidal model structures on ${\mathcal A}$(SO(2)) and R•-mod removes a serious obstruction to constructing a series of monoidal Quillen equivalences between the algebraic model and rational SO(2)–equivariant spectra.

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31

Bardakov, Valeriy G., Andrei V. Lavrenov, and Mikhail V. Neshchadim. "Linearity problem for non-abelian tensor products." Homology, Homotopy and Applications 21, no. 1 (2019): 269–81. http://dx.doi.org/10.4310/hha.2019.v21.n1.a12.

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32

Brown, R., D. L. Johnson, and E. F. Robertson. "Some computations of non-abelian tensor products of groups." Journal of Algebra 111, no. 1 (November 1987): 177–202. http://dx.doi.org/10.1016/0021-8693(87)90248-1.

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33

Conduché, Daniel, and Celso Rodríguez-Fernández. "Non-abelian tensor and exterior products modulo q and universal q-central relative extension." Journal of Pure and Applied Algebra 78, no. 2 (April 1992): 139–60. http://dx.doi.org/10.1016/0022-4049(92)90092-t.

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34

Garat, Alcides. "Tetrads in SU(3) × SU(2) × U(1) Yang–Mills geometrodynamics." International Journal of Geometric Methods in Modern Physics 15, no. 03 (February 20, 2018): 1850045. http://dx.doi.org/10.1142/s0219887818500457.

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The relationship between gauge and gravity amounts to understanding the underlying new geometrical local structures. These structures are new tetrads specially devised for Yang–Mills theories, Abelian and non-Abelian in four-dimensional Lorentzian curved spacetimes. In the present paper, a new tetrad is introduced for the Yang–Mills [Formula: see text] formulation. These new tetrads establish a link between local groups of gauge transformations and local groups of spacetime transformations that we previously called LB1 and LB2. New theorems are proved regarding isomorphisms between local internal [Formula: see text] groups and local tensor products of spacetime LB1 and LB2 groups of transformations. These new tetrads define at every point in spacetime two orthogonal planes that we called blades or planes one and two. These are the local planes of covariant diagonalization of the stress–energy tensor. These tetrads are gauge dependent. Tetrad local gauge transformations leave the tetrads inside the local original planes without leaving them. These local tetrad gauge transformations enable the possibility to connect local gauge groups Abelian or non-Abelian with local groups of tetrad transformations. On the local plane one, the Abelian group [Formula: see text] of gauge transformations was already proved to be isomorphic to the tetrad local group of transformations LB1, for example. LB1 is [Formula: see text] plus two different kinds of discrete transformations. On the local orthogonal plane two [Formula: see text] is isomorphic to LB2 which is just [Formula: see text]. That is, we proved that LB1 is isomorphic to [Formula: see text] which is a remarkable result since a noncompact group plus two discrete transformations is isomorphic to a compact group. These new tetrads have displayed manifestly and nontrivially the coupling between Yang–Mills fields and gravity. The new tetrads and the stress–energy tensor allow for the introduction of three new local gauge invariant objects. Using these new gauge invariant objects and in addition a new general local duality transformation, a new algorithm for the gauge invariant diagonalization of the Yang–Mills stress–energy tensor is developed as an application. This is a paper about grand Standard Model gauge theories — General Relativity gravity unification and grand group unification in four-dimensional curved Lorentzian spacetimes.

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35

Djun, T. P., L. T. Handoko, B. Soegijono, and T. Mart. "Viscosities of gluon dominated QGP model within relativistic non-Abelian hydrodynamics." International Journal of Modern Physics A 30, no. 14 (May 14, 2015): 1550077. http://dx.doi.org/10.1142/s0217751x15500773.

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Based on the first principle calculation, a Lagrangian for the system describing quarks, gluons, and their interactions, is constructed. Ascribed to the existence of dissipative behavior as a consequence of strong interaction within quark–gluon plasma (QGP) matter, auxiliary terms describing viscosities are constituted into the Lagrangian. Through a "kind" of phase transition, gluon field is redefined as a scalar field with four-vector velocity inherently attached. Then, the Lagrangian is elaborated further to produce the energy–momentum tensor of dissipative fluid-like system and the equation of motion (EOM). By imposing the law of energy and momentum conservation, the values of shear and bulk viscosities are analytically calculated. Our result shows that, at the energy level close to hadronization, the bulk viscosity is bigger than shear viscosity. By making use of the conjectured values η/s~1/4π and ζ/s~1, the ratio of bulk to shear viscosity is found to be ζ/η>4π.

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36

Khmaladze, Emzar. "Non-abelian tensor and exterior products modulo $q$ and universal $q$-central relative extension of Lie algebras." Homology, Homotopy and Applications 1, no. 1 (1999): 187–204. http://dx.doi.org/10.4310/hha.1999.v1.n1.a9.

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37

Donadze, Guram, Nick Inassaridze, and Manuel Ladra. "Non-abelian tensor and exterior products of multiplicative Lie rings." Forum Mathematicum 29, no. 3 (January 1, 2017). http://dx.doi.org/10.1515/forum-2015-0096.

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AbstractWe define a non-abelian tensor product of multiplicative Lie rings. This is a new concept providing a common approach to the non-abelian tensor product of groups defined by Brown and Loday and to the non-abelian tensor product of Lie rings defined by Ellis. We also prove an analogue of Miller’s theorem for multiplicative Lie rings.

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38

Moravec, Primož. "The non-abelian tensor product of polycyclic groups is polycyclic." Journal of Group Theory 10, no. 6 (January 20, 2007). http://dx.doi.org/10.1515/jgt.2007.057.

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39

Edalatzadeh, Behrouz, Arash Javan, and Ali Reza Salemkar. "Non-abelian tensor product of precrossed modules in Lie algebras, structure and applications." Communications in Algebra, September 20, 2021, 1–13. http://dx.doi.org/10.1080/00927872.2021.1976788.

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40

Casas, J. M., E. Khmaladze, and N. Pacheco Rego. "On some properties preserved by the non-abelian tensor product of Hom-Lie algebras." Linear and Multilinear Algebra, May 2, 2019, 1–20. http://dx.doi.org/10.1080/03081087.2019.1612833.

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41

Floccari, Salvatore, Lie Fu, and Ziyu Zhang. "On the motive of O’Grady’s ten-dimensional hyper-Kähler varieties." Communications in Contemporary Mathematics, July 17, 2020, 2050034. http://dx.doi.org/10.1142/s0219199720500340.

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We investigate how the motive of hyper-Kähler varieties is controlled by weight-2 (or surface-like) motives via tensor operations. In the first part, we study the Voevodsky motive of singular moduli spaces of semistable sheaves on K3 and abelian surfaces as well as the Chow motive of their crepant resolutions, when they exist. We show that these motives are in the tensor subcategory generated by the motive of the surface, provided that a crepant resolution exists. This extends a recent result of Bülles to the O’Grady-10 situation. In the non-commutative setting, similar results are proved for the Chow motive of moduli spaces of (semi-)stable objects of the K3 category of a cubic fourfold. As a consequence, we provide abundant examples of hyper-Kähler varieties of O’Grady-10 deformation type satisfying the standard conjectures. In the second part, we study the André motive of projective hyper-Kähler varieties. We attach to any such variety its defect group, an algebraic group which acts on the cohomology and measures the difference between the full motive and its weight-2 part. When the second Betti number is not 3, we show that the defect group is a natural complement of the Mumford–Tate group inside the motivic Galois group, and that it is deformation invariant. We prove the triviality of this group for all known examples of projective hyper-Kähler varieties, so that in each case the full motive is controlled by its weight-2 part. As applications, we show that for any variety motivated by a product of known hyper-Kähler varieties, all Hodge and Tate classes are motivated, the motivated Mumford–Tate conjecture 7.3 holds, and the André motive is abelian. This last point completes a recent work of Soldatenkov and provides a different proof for some of his results.

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42

Dao, H. L., and Parinya Karndumri. "$$dS_5$$ vacua from matter-coupled 5D $$N=4$$ gauged supergravity." European Physical Journal C 79, no. 9 (September 2019). http://dx.doi.org/10.1140/epjc/s10052-019-7317-z.

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Abstract We study $$dS_5$$dS5 vacua within matter-coupled $$N=4$$N=4 gauged supergravity in five dimensions using the embedding tensor formalism. With a simple ansatz for solving the extremization and positivity of the scalar potential, we derive a set of conditions for the gauged supergravity to admit $$dS_5$$dS5 as maximally symmetric background solutions. The results provide a new approach for finding $$dS_5$$dS5 vacua in five-dimensional $$N=4$$N=4 gauged supergravity and explain a number of notable features pointed out in previous works. These conditions also determine the form of the gauge groups to be $$SO(1,1)\times G_{\text {nc}}$$SO(1,1)×Gnc with $$G_{\text {nc}}$$Gnc being a non-abelian non-compact group. In general, $$G_{\text {nc}}$$Gnc can be a product of SO(1, 2) and a smaller non-compact group $${G^{\prime }}_{{\text {nc}}}$$G′nc together with (possibly) a compact group. The SO(1, 1) factor is gauged by one of the six graviphotons, that is singlet under $$SO(5)\sim USp(4)$$SO(5)∼USp(4) R-symmetry. The compact parts of SO(1, 2) and $${G^{\prime }}_{{\text {nc}}}$$G′nc are gauged by vector fields from the gravity and vector multiplets, respectively. In addition, we explicitly study $$dS_5$$dS5 vacua for a number of gauge groups and compute scalar masses at the vacua. As in the four-dimensional $$N=4$$N=4 gauged supergravity, all the $$dS_5$$dS5 vacua identified here are unstable.

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43

Bianchi, Lorenzo, Adam Chalabi, Vladimír Procházka, Brandon Robinson, and Jacopo Sisti. "Monodromy defects in free field theories." Journal of High Energy Physics 2021, no. 8 (August 2021). http://dx.doi.org/10.1007/jhep08(2021)013.

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Abstract We study co-dimension two monodromy defects in theories of conformally coupled scalars and free Dirac fermions in arbitrary d dimensions. We characterise this family of conformal defects by computing the one-point functions of the stress-tensor and conserved current for Abelian flavour symmetries as well as two-point functions of the displacement operator. In the case of d = 4, the normalisation of these correlation functions are related to defect Weyl anomaly coefficients, and thus provide crucial information about the defect conformal field theory. We provide explicit checks on the values of the defect central charges by calculating the universal part of the defect contribution to entanglement entropy, and further, we use our results to extract the universal part of the vacuum Rényi entropy. Moreover, we leverage the non-supersymmetric free field results to compute a novel defect Weyl anomaly coefficient in a d = 4 theory of free $$ \mathcal{N} $$ N = 2 hypermultiplets. Including singular modes in the defect operator product expansion of fundamental fields, we identify notable relevant deformations in the singular defect theories and show that they trigger a renormalisation group flow towards an IR fixed point with the most regular defect OPE. We also study Gukov-Witten defects in free d = 4 Maxwell theory and show that their central charges vanish.

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44

NAKAOKA, IRENE N. "Non-abelian tensor products of solvable groups." Journal of Group Theory 3, no. 2 (January 12, 2000). http://dx.doi.org/10.1515/jgth.2000.013.

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45

Nakaoka, Irene, and Romeu Rocco. "Nilpotent actions on non-abelian tensor products of groups." Matemática Contemporânea 21, no. 13 (2001). http://dx.doi.org/10.21711/231766362001/rmc2113.

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46

Moravec, Primož. "Powerful actions and non-abelian tensor products of powerful p-groups." Journal of Group Theory 13, no. 3 (January 2010). http://dx.doi.org/10.1515/jgt.2009.059.

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47

Taha, Tahereh Fakhr, Manuel Ladra, and Pilar Páez-Guillán. "The non-abelian tensor and exterior products of crossed modules of Lie superalgebras." Journal of Algebra and Its Applications, May 31, 2021, 2250169. http://dx.doi.org/10.1142/s0219498822501699.

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In this paper, we introduce the notions of non-abelian tensor and exterior products of two ideal graded crossed submodules of a given crossed module of Lie superalgebras. We also study some of their basic properties and their connection with the second homology of crossed modules of Lie superalgebras.

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48

Nakaoka, Irene N., and Noraí R. Rocco. "A survey of non-abelian tensor products of groups and related constructions." Boletim da Sociedade Paranaense de Matemática 30, no. 1 (March 29, 2012). http://dx.doi.org/10.5269/bspm.v30i1.13350.

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