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Journal articles on the topic 'Bialgebroid'

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Published: 10 December 2022

Last updated: 29 January 2023

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1

Lang, Honglei, Yu Qiao, and Yanbin Yin. "On Lie bialgebroid crossed modules." International Journal of Mathematics 32, no. 04 (March 2021): 2150021. http://dx.doi.org/10.1142/s0129167x2150021x.

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We study Lie bialgebroid crossed modules which are pairs of Lie algebroid crossed modules in duality that canonically give rise to Lie bialgebroids. A one-one correspondence between such Lie bialgebroid crossed modules and co-quadratic Manin triples [Formula: see text] is established, where [Formula: see text] is a co-quadratic Lie algebroid and [Formula: see text] is a pair of transverse Dirac structures in [Formula: see text].

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2

XU, PING. "ON POISSON GROUPOIDS." International Journal of Mathematics 06, no. 01 (February 1995): 101–24. http://dx.doi.org/10.1142/s0129167x95000080.

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Some important properties of Poisson groupoids are discussed. In particular, we obtain a useful formula for the Poisson tensor of an arbitrary Poisson groupoid, which generalizes the well-known multiplicativity condition for Poisson groups. Morphisms between Poisson groupoids and between Lie bialgebroids are also discussed. In particular, for a special class of Lie bialgebroid morphisms, we give an explicit lifting construction. As an application, we prove that a Poisson group action on a Poisson manifold lifts to a Poisson action on its α-simply connected symplectic groupoid.

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3

Cariñena, José F., Janusz Grabowski, and Giuseppe Marmo. "Courant algebroid and Lie bialgebroid contractions." Journal of Physics A: Mathematical and General 37, no. 19 (April 28, 2004): 5189–202. http://dx.doi.org/10.1088/0305-4470/37/19/006.

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4

Kadison, Lars, and Kornél Szlachányi. "Bialgebroid actions on depth two extensions and duality." Advances in Mathematics 179, no. 1 (October 2003): 75–121. http://dx.doi.org/10.1016/s0001-8708(02)00028-2.

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5

Kosmann-Schwarzbach, Yvette. "The lie bialgebroid of a Poisson-Nijenhuis manifold." Letters in Mathematical Physics 38, no. 4 (December 1996): 421–28. http://dx.doi.org/10.1007/bf01815524.

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6

Ṣahin, Bayram, and Fulya Ṣahin. "Generalized almost para-contact manifolds." International Journal of Geometric Methods in Modern Physics 14, no. 10 (September 13, 2017): 1750147. http://dx.doi.org/10.1142/s021988781750147x.

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In this paper, we study generalized almost para-contact manifolds and obtain normality conditions in terms of classical tensor fields. We show that such manifolds naturally carry certain Lie bialgebroid/quasi-Lie algebroid structures on them and we relate these new generalized manifolds with classical almost para-contact manifolds. The paper contains several examples and a short review for relations between generalized geometry and string theory.

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7

ARDIZZONI, A., L. EL KAOUTIT, and C. MENINI. "CATEGORIES OF COMODULES AND CHAIN COMPLEXES OF MODULES." International Journal of Mathematics 23, no. 10 (October 2012): 1250109. http://dx.doi.org/10.1142/s0129167x12501091.

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Let [Formula: see text] denote the coendomorphism left R-bialgebroid associated to a left finitely generated and projective extension of rings R → A with identities. We show that the category of left comodules over an epimorphic image of [Formula: see text] is equivalent to the category of chain complexes of left R-modules. This equivalence is monoidal whenever R is commutative and A is an R-algebra. This is a generalization, using entirely new tools, of results by Pareigis and Tambara for chain complexes of vector spaces over fields. Our approach relies heavily on the noncommutative theory of Tannaka reconstruction, and the generalized faithfully flat descent for small additive categories, or rings with enough orthogonal idempotents.

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8

WANG, YONG, and GUANGQUAN GUO. "SMASH PRODUCTS, SEPARABLE EXTENSIONS AND A MORITA CONTEXT OVER HOPF ALGEBROIDS." Journal of Algebra and Its Applications 13, no. 04 (January 9, 2014): 1350124. http://dx.doi.org/10.1142/s0219498813501247.

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Let [Formula: see text] be a Hopf algebroid, and A a left [Formula: see text]-module algebra. This paper is concerned with the smash product algebra A#H over Hopf algebroids. In this paper, we investigate separable extensions for module algebras over Hopf algebroids. As an application, we obtain a Maschke-type theorem for A#H-modules over Hopf algebroids, which generalizes the corresponding result given by Cohen and Fischman in [Hopf algebra actions, J. Algebra100 (1986) 363–379]. Furthermore, based on the work of Kadison and Szlachányi in [Bialgebroid actions on depth two extensions and duality, Adv. Math.179 (2003) 75–121], we construct a Morita context connecting A#H and [Formula: see text] the invariant subalgebra of [Formula: see text] on A.

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9

Jurić, Tajron, Stjepan Meljanac, and Rina Štrajn. "Twists, realizations and Hopf algebroid structure of κ-deformed phase space." International Journal of Modern Physics A 29, no. 05 (February 18, 2014): 1450022. http://dx.doi.org/10.1142/s0217751x14500225.

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The quantum phase space described by Heisenberg algebra possesses undeformed Hopf algebroid structure. The κ-deformed phase space with noncommutative coordinates is realized in terms of undeformed quantum phase space. There are infinitely many such realizations related by similarity transformations. For a given realization, we construct corresponding coproducts of commutative coordinates and momenta (bialgebroid structure). The κ-deformed phase space has twisted Hopf algebroid structure. General method for the construction of twist operator (satisfying cocycle and normalization condition) corresponding to deformed coalgebra structure is presented. Specially, twist for natural realization (classical basis) of κ-Minkowski space–time is presented. The cocycle condition, κ-Poincaré algebra and R-matrix are discussed. Twist operators in arbitrary realizations are constructed from the twist in the given realization using similarity transformations. Some examples are presented. The important physical applications of twists, realizations, R-matrix and Hopf algebroid structure are discussed.

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10

Femić, Bojana. "Eilenberg–Watts Theorem for 2-categories and quasi-monoidal structures for module categories over bialgebroid categories." Journal of Pure and Applied Algebra 220, no. 9 (September 2016): 3156–81. http://dx.doi.org/10.1016/j.jpaa.2016.02.009.

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11

Borowiec, Andrzej, and Anna Pachoł. "Twisted bialgebroids versus bialgebroids from a Drinfeld twist." Journal of Physics A: Mathematical and Theoretical 50, no. 5 (January 6, 2017): 055205. http://dx.doi.org/10.1088/1751-8121/50/5/055205.

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12

ARDIZZONI, A., L. EL KAOUTIT, and C. MENINI. "COENDOMORPHISM LEFT BIALGEBROIDS." Journal of Algebra and Its Applications 12, no. 03 (December 20, 2012): 1250181. http://dx.doi.org/10.1142/s0219498812501812.

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The main purpose of this paper is to give a rigorous proof of the construction of coendomorphism left bialgebroids as well as an explicit description of their structure maps. We also compute some concrete examples of these objects by means of their generators and relations.

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13

Mackenzie, Kirill C. H., and Ping Xu. "Integration of Lie bialgebroids." Topology 39, no. 3 (May 2000): 445–67. http://dx.doi.org/10.1016/s0040-9383(98)00069-x.

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14

Mackenzie, Kirill C. H., and Ping Xu. "Lie bialgebroids and Poisson groupoids." Duke Mathematical Journal 73, no. 2 (February 1994): 415–52. http://dx.doi.org/10.1215/s0012-7094-94-07318-3.

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15

Szlachányi, Kornél. "Skew-monoidal categories and bialgebroids." Advances in Mathematics 231, no. 3-4 (October 2012): 1694–730. http://dx.doi.org/10.1016/j.aim.2012.06.027.

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16

Liu, Zhang-Ju, Alan Weinstein, and Ping Xu. "Manin triples for Lie bialgebroids." Journal of Differential Geometry 45, no. 3 (1997): 547–74. http://dx.doi.org/10.4310/jdg/1214459842.

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17

Lean, M. Jotz. "Dirac groupoids and Dirac bialgebroids." Journal of Symplectic Geometry 17, no. 1 (2019): 179–238. http://dx.doi.org/10.4310/jsg.2019.v17.n1.a4.

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18

Brzeziński, Tomasz, and Gigel Militaru. "Bialgebroids, ×A-Bialgebras and Duality." Journal of Algebra 251, no. 1 (May 2002): 279–94. http://dx.doi.org/10.1006/jabr.2001.9101.

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19

Bao-Kang, Liu, and He Long-Guang. "Dirac-nijenhuis structures on lie bialgebroids." Reports on Mathematical Physics 55, no. 2 (April 2005): 179–98. http://dx.doi.org/10.1016/s0034-4877(05)00010-8.

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20

Iglesias, David, and Juan C. Marrero. "Generalized Lie bialgebroids and Jacobi structures." Journal of Geometry and Physics 40, no. 2 (December 2001): 176–200. http://dx.doi.org/10.1016/s0393-0440(01)00032-8.

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21

Iglesias-Ponte, David, and Juan C. Marrero. "Jacobi groupoids and generalized Lie bialgebroids." Journal of Geometry and Physics 48, no. 2-3 (November 2003): 385–425. http://dx.doi.org/10.1016/s0393-0440(03)00050-0.

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22

Kosmann-Schwarzbach, Y. "Exact Gerstenhaber algebras and Lie bialgebroids." Acta Applicandae Mathematicae 41, no. 1-3 (December 1995): 153–65. http://dx.doi.org/10.1007/bf00996111.

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23

Liu, Z. J., and P. Xu. "Exact lie bialgebroids and poisson groupoids." Geometric and Functional Analysis 6, no. 1 (January 1996): 138–45. http://dx.doi.org/10.1007/bf02246770.

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24

Poon, Yat Sun, and Aïssa Wade. "Lie bialgebroids of generalized CRF-manifolds." Comptes Rendus Mathematique 348, no. 15-16 (August 2010): 919–22. http://dx.doi.org/10.1016/j.crma.2010.07.005.

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25

Costa, J. M. Nunes da, and J. Clemente-Gallardo. "Dirac structures for generalized Lie bialgebroids." Journal of Physics A: Mathematical and General 37, no. 7 (February 4, 2004): 2671–92. http://dx.doi.org/10.1088/0305-4470/37/7/011.

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26

Plotkin, Gordon. "Bialgebraic Semantics and Recursion." Electronic Notes in Theoretical Computer Science 44, no. 1 (May 2001): 285–88. http://dx.doi.org/10.1016/s1571-0661(04)80914-9.

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27

Kearnes, Keith A., and Frank Vogt. "Bialgebraic contexts from dualities." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 60, no. 3 (June 1996): 389–404. http://dx.doi.org/10.1017/s1446788700037897.

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AbstractIn this paper we show that a bialgebraic context which arises from a duality in a fairly general way must arise from a duality between categories of modules. To show this, we give an elementary proof of Mitchell's Embedding Theorem for prevarieties.

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28

Szlachányi, Kornél. "The monoidal Eilenberg–Moore construction and bialgebroids." Journal of Pure and Applied Algebra 182, no. 2-3 (August 2003): 287–315. http://dx.doi.org/10.1016/s0022-4049(03)00018-5.

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29

Nunes da Costa, J. M., and F. Petalidou. "On Quasi-Jacobi and Jacobi-Quasi Bialgebroids." Letters in Mathematical Physics 80, no. 2 (April 5, 2007): 155–69. http://dx.doi.org/10.1007/s11005-007-0151-5.

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30

Chen, Z., and Z. J. Liu. "On transitive Lie bialgebroids and Poisson groupoids." Differential Geometry and its Applications 22, no. 3 (May 2005): 253–74. http://dx.doi.org/10.1016/j.difgeo.2005.01.001.

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31

Rot, Jurriaan, and Marcello Bonsangue. "Structural congruence for bialgebraic semantics." Journal of Logical and Algebraic Methods in Programming 85, no. 6 (October 2016): 1268–91. http://dx.doi.org/10.1016/j.jlamp.2016.08.001.

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32

Iglesias, David, Belen Lopez, Juan C. Marrero, and Edith Padron. "Triangular generalized Lie bialgebroids: Homology and cohomology theories." Banach Center Publications 54 (2001): 111–33. http://dx.doi.org/10.4064/bc54-0-8.

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33

Liu, Jiefeng, Yunhe Sheng, and Chengming Bai. "Left-symmetric bialgebroids and their corresponding Manin triples." Differential Geometry and its Applications 59 (August 2018): 91–111. http://dx.doi.org/10.1016/j.difgeo.2018.04.003.

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34

Klin, Bartek. "From Bialgebraic Semantics to Congruence Formats." Electronic Notes in Theoretical Computer Science 128, no. 1 (May 2005): 3–37. http://dx.doi.org/10.1016/j.entcs.2004.09.038.

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35

Klin, Bartek. "Bialgebraic Methods in Structural Operational Semantics." Electronic Notes in Theoretical Computer Science 175, no. 1 (May 2007): 33–43. http://dx.doi.org/10.1016/j.entcs.2006.11.018.

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36

Vogt, F. "Bialgebraic contexts for finite distributive lattices." Algebra Universalis 35, no. 1 (March 1996): 151–65. http://dx.doi.org/10.1007/bf01190975.

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37

Klin, Bartek. "Adding recursive constructs to bialgebraic semantics." Journal of Logic and Algebraic Programming 60-61 (July 2004): 259–86. http://dx.doi.org/10.1016/j.jlap.2004.03.005.

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38

Hassanzadeh, Mohammad. "On Cyclic Cohomology of ×-Hopf algebras." Journal of K-Theory 13, no. 1 (January 2, 2014): 147–70. http://dx.doi.org/10.1017/is013011021jkt246.

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AbstractIn this paper we study the cyclic cohomology of certain ×-Hopf algebras: universal enveloping algebras, quantum algebraic tori, the Connes-Moscovici ×-Hopf algebroids and the Kadison bialgebroids. Introducing their stable anti Yetter-Drinfeld modules and cocyclic modules, we compute their cyclic cohomology. Furthermore, we provide a pairing for the cyclic cohomology of ×-Hopf algebras which generalizes the Connes-Moscovici characteristic map to ×-Hopf algebras. This enables us to transfer the ×-Hopf algebra cyclic cocycles to algebra cyclic cocycles.

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39

Pridham, J. P. "Deformations of schemes and other bialgebraic structures." Transactions of the American Mathematical Society 360, no. 03 (March 1, 2008): 1601–30. http://dx.doi.org/10.1090/s0002-9947-07-04355-3.

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40

Wang, Xiaomeng, Shou-Jun Xu, and Xing Gao. "A Hopf algebra on subgraphs of a graph." Journal of Algebra and Its Applications 19, no. 09 (August 26, 2019): 2050164. http://dx.doi.org/10.1142/s0219498820501649.

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In this paper, we construct a bialgebraic and further a Hopf algebraic structure on top of subgraphs of a given graph. Further, we give the dual structure of this Hopf algebraic structure. We study the algebra morphisms induced by graph homomorphisms, and obtain a covariant functor from a graph category to an algebra category.

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41

Kadison, Lars. "Galois theory for bialgebroids, depth two and normal Hopf subalgebras." ANNALI DELL UNIVERSITA DI FERRARA 51, no. 1 (January 2005): 209–31. http://dx.doi.org/10.1007/bf02824832.

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42

Cai, Liqiang, Jiefeng Liu, and Yunhe Sheng. "Hom-Lie algebroids, Hom-Lie bialgebroids and Hom-Courant algebroids." Journal of Geometry and Physics 121 (November 2017): 15–32. http://dx.doi.org/10.1016/j.geomphys.2017.07.006.

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43

Kowalzig, Niels. "Batalin–Vilkovisky algebra structures on (Co)Tor and Poisson bialgebroids." Journal of Pure and Applied Algebra 219, no. 9 (September 2015): 3781–822. http://dx.doi.org/10.1016/j.jpaa.2014.12.022.

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44

Panaite, Florin, and Freddy Van Oystaeyen. "Some Bialgebroids Constructed by Kadison and Connes–Moscovici are Isomorphic." Applied Categorical Structures 14, no. 5-6 (November 15, 2006): 627–32. http://dx.doi.org/10.1007/s10485-006-9052-5.

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45

Mosrijai, Phakawat, and Aiyared Iampan. "A new branch of bialgebraic structures: UP-bialgebras." Journal of Taibah University for Science 13, no. 1 (March 19, 2019): 450–59. http://dx.doi.org/10.1080/16583655.2019.1592932.

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46

Cioroianu, Eugen-Mihaita, and Cornelia Vizman. "Jacobi structures with background." International Journal of Geometric Methods in Modern Physics 17, no. 04 (March 2020): 2050063. http://dx.doi.org/10.1142/s0219887820500632.

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Combining the twisted Jacobi structure [Twisted Jacobi manifolds, twisted Dirac–Jacobi structures and quasi-Jacobi bialgebroids, J. Phys. A: Math. Gen. 39(33) (2006) 10449–10475] with that of a Poisson structure with a 3-form background [Poisson geometry with a 3-form background, Prog. Theor. Phys. Suppl. 144 (2001) 145–154], alias twisted Poisson, we propose and analyze a new structure, called Jacobi structure with background. The background is a pair consisting of a [Formula: see text]-form and a [Formula: see text]-form. We describe their characteristic leaves. For twisted contact dual pairs, we show the correspondence of characteristic leaves of the two Jacobi manifolds with background.

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47

Bischoff, Francis, Henrique Bursztyn, Hudson Lima, and Eckhard Meinrenken. "Deformation spaces and normal forms around transversals." Compositio Mathematica 156, no. 4 (February 17, 2020): 697–732. http://dx.doi.org/10.1112/s0010437x1900784x.

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Given a manifold $M$ with a submanifold $N$, the deformation space ${\mathcal{D}}(M,N)$ is a manifold with a submersion to $\mathbb{R}$ whose zero fiber is the normal bundle $\unicode[STIX]{x1D708}(M,N)$, and all other fibers are equal to $M$. This article uses deformation spaces to study the local behavior of various geometric structures associated with singular foliations, with $N$ a submanifold transverse to the foliation. New examples include $L_{\infty }$-algebroids, Courant algebroids, and Lie bialgebroids. In each case, we obtain a normal form theorem around $N$, in terms of a model structure over $\unicode[STIX]{x1D708}(M,N)$.

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48

Mackenzie, K. C. H. "Drinfel’d doubles and Ehresmann doubles for Lie algebroids and Lie bialgebroids." Electronic Research Announcements of the American Mathematical Society 4, no. 11 (October 22, 1998): 74–87. http://dx.doi.org/10.1090/s1079-6762-98-00050-x.

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49

Böhm, Gabriella, and Dragoş Ştefan. "(Co)cyclic (Co)homology of Bialgebroids: An Approach via (Co)monads." Communications in Mathematical Physics 282, no. 1 (June 17, 2008): 239–86. http://dx.doi.org/10.1007/s00220-008-0540-3.

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50

Costa, J. M. Nunes da, and F. Petalidou. "Twisted Jacobi manifolds, twisted Dirac–Jacobi structures and quasi-Jacobi bialgebroids." Journal of Physics A: Mathematical and General 39, no. 33 (August 2, 2006): 10449–75. http://dx.doi.org/10.1088/0305-4470/39/33/014.

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