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Journal articles on the topic 'Quantum superalgebras'

Author: Grafiati

Published: 4 June 2021

Last updated: 13 February 2022

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1

RASMUSSEN, JØRGEN. "SCREENING CURRENT REPRESENTATION OF QUANTUM SUPERALGEBRAS." Modern Physics Letters A 13, no. 18 (June 14, 1998): 1485–93. http://dx.doi.org/10.1142/s021773239800156x.

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In this letter a screening current or contour representation is given for certain quantum superalgebras. The Gomez–Sierra construction of quantum groups in conformal field theory is generalized to cover superalgebras and illustrated using recent results on screening currents in affine current superalgebra.

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2

DU, JIE, and JINKUI WAN. "THE QUEER -SCHUR SUPERALGEBRA." Journal of the Australian Mathematical Society 105, no. 3 (February 2, 2018): 316–46. http://dx.doi.org/10.1017/s1446788717000337.

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As a natural generalisation of $q$-Schur algebras associated with the Hecke algebra ${\mathcal{H}}_{r,R}$ (of the symmetric group), we introduce the queer $q$-Schur superalgebra associated with the Hecke–Clifford superalgebra ${\mathcal{H}}_{r,R}^{\mathsf{c}}$, which, by definition, is the endomorphism algebra of the induced ${\mathcal{H}}_{r,R}^{\mathsf{c}}$-module from certain $q$-permutation modules over ${\mathcal{H}}_{r,R}$. We will describe certain integral bases for these superalgebras in terms of matrices and will establish the base-change property for them. We will also identify the queer $q$-Schur superalgebras with the quantum queer Schur superalgebras investigated in the context of quantum queer supergroups and provide a constructible classification of their simple polynomial representations over a certain extension of the field $\mathbb{C}(\mathbf{v})$ of complex rational functions.

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3

DELIUS, GUSTAV W., MARK D. GOULD, JON R. LINKS, and YAO-ZHONG ZHANG. "ON TYPE I QUANTUM AFFINE SUPERALGEBRAS." International Journal of Modern Physics A 10, no. 23 (September 20, 1995): 3259–81. http://dx.doi.org/10.1142/s0217751x95001571.

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The type I simple Lie superalgebras are sl(m|n) and osp(2|2n). We study the quantum deformations of their untwisted affine extensions Uq[sl(m|n)(1)] and Uq[osp(2|2n)(1)]. We identify additional relations between the simple generators (“extra q Serre relations”) which need to be imposed in order to properly define Uq[sl(m|n)(1)] and Uq[osp(2|2n)(1)]. We present a general technique for deriving the spectral-parameter-dependent R matrices from quantum affine superalgebras. We determine the R matrices for the type I affine superalgebra Uq[sl(m|n)(1)] in various representations, thereby deriving new solutions of the spectral-parameter-dependent Yang-Baxter equation. In particular, because this algebra possesses one-parameter families of finite-dimensional irreps, we are able to construct R matrices depending on two additional spectral-parameter-like parameters, providing generalizations of the free fermion model.

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4

GOULD, MARK D., and YAO-ZHONG ZHANG. "R-MATRICES AND THE TENSOR PRODUCT GRAPH METHOD." International Journal of Modern Physics B 16, no. 14n15 (June 20, 2002): 2145–51. http://dx.doi.org/10.1142/s0217979202011901.

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A systematic method for constructing trigonometric R-matrices corresponding to the (multiplicity-free) tensor product of any two affinizable representations of a quantum algebra or superalgebra has been developed by the Brisbane group and its collaborators. This method has been referred to as the Tensor Product Graph Method. Here we describe applications of this method to untwisted and twisted quantum affine superalgebras.

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5

ITO, KATSUSHI. "QUANTUM HAMILTONIAN REDUCTION AND WB ALGEBRA." International Journal of Modern Physics A 07, no. 20 (August 10, 1992): 4885–98. http://dx.doi.org/10.1142/s0217751x92002210.

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We study the quantum Hamiltonian reduction of affine Lie algebras and the free field realization of the associated W algebra. For the nonsimply laced case this reduction does not agree with the usual coset construction of the W minimal model. In particular, we find that the coset model [Formula: see text] can be obtained through the quantum Hamiltonian reduction of the affine Lie superalgebra B(0, n)(1). To show this we also construct the Feigin-Fuchs representation of affine Lie superalgebras.

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6

BOROWIEC, A., J. LUKIERSKI, and V. N. TOLSTOY. "BASIC TWIST QUANTIZATION OF osp(1|2) AND κ-DEFORMATION OF D = 1 SUPERCONFORMAL MECHANICS." Modern Physics Letters A 18, no. 17 (June 7, 2003): 1157–69. http://dx.doi.org/10.1142/s021773230301096x.

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The twisting function describing a nonstandard (super-Jordanian) quantum deformation of osp (1|2) is given in explicit closed form. The quantum coproducts and universal R-matrix are presented. The non-uniqueness of the twisting function as well as two real forms of the deformed osp (1|2) superalgebras are considered. One real quantum osp (1|2) superalgebra is interpreted as describing the κ-deformation of D = 1, N = 1 superconformal algebra, which can be applied as a symmetry algebra of N = 1 superconformal mechanics.

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7

HEIDENREICH, WOLFGANG, and JERZY LUKIERSKI. "QUANTIZED SUPERTWISTORS, HIGHER SPIN SUPERALGEBRAS AND SUPERSINGLETONS." Modern Physics Letters A 05, no. 06 (March 10, 1990): 439–51. http://dx.doi.org/10.1142/s0217732390000512.

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We introduce supertwistors in D=3 and D=4 as describing the canonical coordinates in two models of fundamental phase space with respectively OSP(N; 4) and u(2, 2; N) invariant fundamental Poisson brackets. The infinite superalgebra of normally ordered polynomials in quantized supertwistor variables can be identified with recently proposed D=3 and D=4 higher spin superalgebras. We consider the supersingleton representations of OSP(N, 4), and OSP(2N, 8) as describing fundamental realizations of D=3 and D=4 supertwistor quantum mechanics.

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8

耿, 亚娜. "Coordinate Superalgebras of Quantum Superalgebras Based on the RTT Relation." Pure Mathematics 10, no. 12 (2020): 1213–19. http://dx.doi.org/10.12677/pm.2020.1012144.

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9

Zhang, Huafeng. "Representations of quantum affine superalgebras." Mathematische Zeitschrift 278, no. 3-4 (June 10, 2014): 663–703. http://dx.doi.org/10.1007/s00209-014-1330-6.

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10

Kac, Victor, Shi-Shyr Roan, and Minoru Wakimoto. "Quantum Reduction for Affine Superalgebras." Communications in Mathematical Physics 241, no. 2-3 (September 12, 2003): 307–42. http://dx.doi.org/10.1007/s00220-003-0926-1.

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11

Benkart, Georgia, Nicolas Guay, Ji Hye Jung, Seok-Jin Kang, and Stewart Wilcox. "Quantum walled Brauer–Clifford superalgebras." Journal of Algebra 454 (May 2016): 433–74. http://dx.doi.org/10.1016/j.jalgebra.2015.04.038.

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12

SPECTOR, DONALD. "BPS AND DUALITY IN SUPERSYMMETRIC QUANTUM MECHANICS." International Journal of Modern Physics A 20, no. 27 (October 30, 2005): 6288–97. http://dx.doi.org/10.1142/s0217751x05029319.

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This paper explores the consequences of superalgebras with central charges in the context of non-relativistic quantum mechanics. We find the emergence of target space duality structures in these theories. We also demonstrate that shape invariance is understood most naturally in the context of such centrally extended superalgebras, with their exact solvability a consequence of a BPS structure.

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13

NOWICKI, ANATOL. "STRANGE SUPERALGEBRAS AND DESCRIPTION OF NONRELATIVISTIC SPIN." Modern Physics Letters A 03, no. 02 (January 1988): 179–85. http://dx.doi.org/10.1142/s0217732388000210.

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We show that the supersymmetric structure of the nonrelativistic quantum spin is given by the strange superalgebra of the type [Formula: see text]. The description of the spin particle proposed by Berezin and Marinov is provided by the representation of the real strange superalgebra [Formula: see text]. Different description of quantum spin based on the real quaternionic strange superalgebra [Formula: see text] is also investigated.

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14

Zhang, R. B. "Quantum enveloping superalgebras and link invariants." Journal of Mathematical Physics 43, no. 4 (April 2002): 2029–48. http://dx.doi.org/10.1063/1.1436564.

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15

Xu, Ying, and R. B. Zhang. "Quantum correspondences of affine Lie superalgebras." Mathematical Research Letters 25, no. 3 (2018): 1009–36. http://dx.doi.org/10.4310/mrl.2018.v25.n3.a14.

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16

Liao, Li, and Xingchang Song. "q -Oscillators and Quantum Lie superalgebras." Communications in Theoretical Physics 16, no. 2 (September 1991): 249–56. http://dx.doi.org/10.1088/0253-6102/16/2/249.

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17

Jeong, Kyeonghoon, and Dong-Il Lee. "Integrable Representations of Quantum Borcherds Superalgebras." Communications in Algebra 37, no. 10 (October 9, 2009): 3632–42. http://dx.doi.org/10.1080/00927870902828827.

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18

Malik, R. P. "Cohomological operators and covariant quantum superalgebras." Journal of Physics A: Mathematical and General 37, no. 34 (August 12, 2004): 8383–99. http://dx.doi.org/10.1088/0305-4470/37/34/013.

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19

Hill, David, and Weiqiang Wang. "Categorification of quantum Kac-Moody superalgebras." Transactions of the American Mathematical Society 367, no. 2 (October 23, 2014): 1183–216. http://dx.doi.org/10.1090/s0002-9947-2014-06128-x.

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20

Chang, Zhihua, and Yongjie Wang. "Howe duality for quantum queer superalgebras." Journal of Algebra 547 (April 2020): 358–78. http://dx.doi.org/10.1016/j.jalgebra.2019.11.023.

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21

Chaichian, M., and P. Kulish. "Quantum lie superalgebras and q-oscillators." Physics Letters B 234, no. 1-2 (January 1990): 72–80. http://dx.doi.org/10.1016/0370-2693(90)92004-3.

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22

Accardi, Luigi, Michael Schürmann, and Wilhelm von Waldenfels. "Quantum independent increment processes on superalgebras." Mathematische Zeitschrift 198, no. 4 (December 1988): 451–77. http://dx.doi.org/10.1007/bf01162868.

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23

Bezerra, Luan, and Evgeny Mukhin. "Braid actions on quantum toroidal superalgebras." Journal of Algebra 585 (November 2021): 338–69. http://dx.doi.org/10.1016/j.jalgebra.2021.06.012.

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24

Mansour, M., M. Daoud, and Y. Hassouni. "k-fractional spin through quantum algebras and quantum superalgebras." Physics Letters B 454, no. 3-4 (May 1999): 281–89. http://dx.doi.org/10.1016/s0370-2693(99)00371-8.

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25

DU, JIE, HAIXIA GU, and ZHONGGUO ZHOU. "MULTIPLICATION FORMULAS AND SEMISIMPLICITY FOR -SCHUR SUPERALGEBRAS." Nagoya Mathematical Journal 237 (April 30, 2018): 98–126. http://dx.doi.org/10.1017/nmj.2018.12.

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We investigate products of certain double cosets for the symmetric group and use the findings to derive some multiplication formulas for the $q$-Schur superalgebras. This gives a combinatorialization of the relative norm approach developed in Du and Gu (A realization of the quantum supergroup$\mathbf{U}(\mathfrak{g}\mathfrak{l}_{m|n})$, J. Algebra 404 (2014), 60–99). We then give several applications of the multiplication formulas, including the matrix representation of the regular representation and a semisimplicity criterion for $q$-Schur superalgebras. We also construct infinitesimal and little $q$-Schur superalgebras directly from the multiplication formulas and develop their semisimplicity criteria.

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26

BAKER, T. H., and P. D. JARVIS. "QUANTUM SUPERSPIN CHAINS." International Journal of Modern Physics B 08, no. 25n26 (November 1994): 3623–35. http://dx.doi.org/10.1142/s0217979294001536.

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Supersymmetric formulations of spin-½ quantum chains, associated with integrable models, are considered. One class of super-extensions, based on low-dimensional classical and exceptional superalgebras containing sl(2), is illustrated with the case of osp(1/2). A more radical generalization, in which the algebra of Pauli matrices is identified with the algebra of supersymmetric quantum mechanics, is also presented, and some of its algebraic properties discussed.

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27

Ai, Chunrui, and Shilin Yang. "Two-parameter Quantum Superalgebras and PBW Theorem." Algebra Colloquium 23, no. 02 (March 16, 2016): 303–24. http://dx.doi.org/10.1142/s1005386716000328.

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A class of two-parameter quantum algebras [Formula: see text] is constructed. It is shown that [Formula: see text] is a Hopf superalgebra. Then the PBW basis of [Formula: see text] is described. For this purpose, some commutative relations of root vectors of [Formula: see text] are given.

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28

Hegazi, A., and M. Mansour. "Two-parameter quantum deformation of Lie superalgebras." Chaos, Solitons & Fractals 12, no. 3 (January 3, 2001): 445–52. http://dx.doi.org/10.1016/s0960-0779(99)00191-5.

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29

Ye, Lixia, and Fang Li. "Weak quantum Borcherds superalgebras and their representations." Journal of Mathematical Physics 48, no. 2 (February 2007): 023502. http://dx.doi.org/10.1063/1.2436732.

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30

Du, Jie, and Hebing Rui. "Quantum Schur superalgebras and Kazhdan–Lusztig combinatorics." Journal of Pure and Applied Algebra 215, no. 11 (November 2011): 2715–37. http://dx.doi.org/10.1016/j.jpaa.2011.03.015.

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31

Zhang, R. B. "Symmetrizable quantum affine superalgebras and their representations." Journal of Mathematical Physics 38, no. 1 (January 1997): 535–43. http://dx.doi.org/10.1063/1.531833.

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32

Zhang, Yao-Zhong, and Mark D. Gould. "Quasi-Hopf superalgebras and elliptic quantum supergroups." Journal of Mathematical Physics 40, no. 10 (October 1999): 5264–82. http://dx.doi.org/10.1063/1.533029.

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33

Beckers, J., and N. Debergh. "On colour superalgebras in parasupersymmetric quantum mechanics." Journal of Physics A: Mathematical and General 24, no. 11 (June 7, 1991): L597—L603. http://dx.doi.org/10.1088/0305-4470/24/11/005.

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34

Floreanini, Roberto, Dimitry A. Leites, and Luc Vinet. "On the defining relations of quantum superalgebras." Letters in Mathematical Physics 23, no. 2 (October 1991): 127–31. http://dx.doi.org/10.1007/bf00703725.

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35

Wu, Zhixiang. "Weak Quantum Enveloping Algebras of Borcherds Superalgebras." Acta Applicandae Mathematicae 106, no. 2 (August 13, 2008): 185–98. http://dx.doi.org/10.1007/s10440-008-9289-0.

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36

BENKART, GEORGIA, XIAOPING XU, and KAIMING ZHAO. "CLASSICAL LIE SUPERALGEBRAS OVER SIMPLE ASSOCIATIVE ALGEBRAS." Proceedings of the London Mathematical Society 92, no. 3 (April 18, 2006): 581–600. http://dx.doi.org/10.1017/s0024611505015583.

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Over arbitrary fields of characteristic not equal to 2, we construct three families of simple Lie algebras and six families of simple Lie superalgebras of matrices with entries chosen from different one-sided ideals of a simple associative algebra. These families correspond to the classical Lie algebras and superalgebras. Our constructions intermix the structure of the associative algebra and the structure of the matrix algebra in an essential, compatible way. Many examples of simple associative algebras without an identity element arise as a by-product. The study of conformal algebras and superalgebras often involves matrix algebras over associative algebras such as Weyl algebras, and for that reason, we illustrate our constructions by taking various one-sided ideals from a Weyl algebra or a quantum torus.

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37

DELDUC, F., F. GIERES, S. GOURMELEN, and S. THEISEN. "NONSTANDARD MATRIX FORMATS OF LIE SUPERALGEBRAS." International Journal of Modern Physics A 14, no. 25 (October 10, 1999): 4043–60. http://dx.doi.org/10.1142/s0217751x99001895.

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The standard format of matrices belonging to Lie superalgebras consists of partitioning the matrices into even and odd blocks. In this paper, we present a systematic study of other possible matrix formats and in particular of the so-called diagonal format which naturally occurs in various physical applications, e.g. for the supersymmetric versions of conformal field theory, integrable models. W algebras and quantum groups.

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38

Frappat, L., A. Sciarrino, S. Sciuto, and P. Sorba. "Anyonic realization of the quantum affine Lie superalgebras." Journal of Physics A: Mathematical and General 30, no. 3 (February 7, 1997): 903–14. http://dx.doi.org/10.1088/0305-4470/30/3/015.

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39

Palev, Tchavdar D. "Lie superalgebras, infinite-dimensional algebras and quantum statistics." Reports on Mathematical Physics 31, no. 3 (June 1992): 241–62. http://dx.doi.org/10.1016/0034-4877(92)90017-u.

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40

Sergeev, A. N., and A. P. Veselov. "Deformed Quantum Calogero-Moser Problems and Lie Superalgebras." Communications in Mathematical Physics 245, no. 2 (March 1, 2004): 249–78. http://dx.doi.org/10.1007/s00220-003-1012-4.

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41

BUFFON, L. O., A. ZADRA, and D. DALMAZI. "CLASSICAL AND QUANTUM N=1 SUPER W∞-ALGEBRAS." Modern Physics Letters A 11, no. 29 (September 21, 1996): 2339–49. http://dx.doi.org/10.1142/s0217732396002332.

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We construct higher-spin N=1 superalgebras as extensions of the super-Virasoro algebra containing generators for all spins s≥3/2. We find two distinct classical (Poisson) algebras on the phase superspace. Our results indicate that only one of them can be consistently quantized.

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42

GEER, NATHAN, and BERTRAND PATUREAU-MIRAND. "MULTIVARIABLE LINK INVARIANTS ARISING FROM LIE SUPERALGEBRAS OF TYPE I." Journal of Knot Theory and Its Ramifications 19, no. 01 (January 2010): 93–115. http://dx.doi.org/10.1142/s0218216510007784.

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In this paper, we construct new links invariants from a type I basic Lie superalgebra 𝔤. The construction uses the existence of an unexpected replacement of the vanishing quantum dimension of typical module, by non-trivial "fake quantum dimensions". Using this, we get a multivariable link invariant associated to any one parameter family of irreducible 𝔤-modules.

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43

Bouchard, Vincent, Paweł Ciosmak, Leszek Hadasz, Kento Osuga, Błażej Ruba, and Piotr Sułkowski. "Super Quantum Airy Structures." Communications in Mathematical Physics 380, no. 1 (October 13, 2020): 449–522. http://dx.doi.org/10.1007/s00220-020-03876-0.

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Abstract We introduce super quantum Airy structures, which provide a supersymmetric generalization of quantum Airy structures. We prove that to a given super quantum Airy structure one can assign a unique set of free energies, which satisfy a supersymmetric generalization of the topological recursion. We reveal and discuss various properties of these supersymmetric structures, in particular their gauge transformations, classical limit, peculiar role of fermionic variables, and graphical representation of recursion relations. Furthermore, we present various examples of super quantum Airy structures, both finite-dimensional—which include well known superalgebras and super Frobenius algebras, and whose classification scheme we also discuss—as well as infinite-dimensional, that arise in the realm of vertex operator super algebras.

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44

Chang, D., I. Phillips, and L. Rozansky. "R‐matrix approach to quantum superalgebras suq(m‖n)." Journal of Mathematical Physics 33, no. 11 (November 1992): 3710–15. http://dx.doi.org/10.1063/1.529866.

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45

Hakobyan, T. S., and A. G. Sedrakyan. "Universal R matrix of Uqsl(n,m) quantum superalgebras." Journal of Mathematical Physics 35, no. 5 (May 1994): 2552–59. http://dx.doi.org/10.1063/1.530522.

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46

Baulieu, Laurent, and Francesco Toppan. "Twisted superalgebras and cohomologies of the superconformal quantum mechanics." Nuclear Physics B 855, no. 3 (February 2012): 742–59. http://dx.doi.org/10.1016/j.nuclphysb.2011.10.022.

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47

LIAO, LI, and XING-CHANG SONG. "QUANTUM LIE SUPERALGEBRAS AND “NON-STANDARD” BRAID GROUP REPRESENTATIONS." Modern Physics Letters A 06, no. 11 (April 10, 1991): 959–68. http://dx.doi.org/10.1142/s0217732391001007.

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The formulae of the Faddeev-Reshetikhin-Takhtajan (FRT) method in supersymmetric case are presented transparently and consistently. With the help of these formulae, the simplest “non-standard” solution of braid group representation (BGR) is re-examined. The result shows that the hidden symmetry associated with this “non-standard” BGR is indeed the q-deformed Lie superalgebra U q ( gl (1|1)).

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48

Zhang, Huafeng. "RTT Realization of Quantum Affine Superalgebras and Tensor Products." International Mathematics Research Notices 2016, no. 4 (June 4, 2015): 1126–57. http://dx.doi.org/10.1093/imrn/rnv167.

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49

Gould, M. D., J. R. Links, and Y. Z. Zhang. "Eigenvalues of Casimir invariants for type I quantum superalgebras." Letters in Mathematical Physics 36, no. 4 (April 1996): 415–25. http://dx.doi.org/10.1007/bf00714406.

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50

Liu, Jun Li, and Shi Lin Yang. "Orthosymplectic quantum function superalgebras OSP q (2l+1|2n)." Acta Mathematica Sinica, English Series 27, no. 5 (April 15, 2011): 983–1004. http://dx.doi.org/10.1007/s10114-011-8037-y.

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