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Relevant bibliographies by topics / Twisted bialgebra

Academic literature on the topic 'Twisted bialgebra'

Author: Grafiati

Published: 17 February 2024

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Journal articles on the topic "Twisted bialgebra"

1

Song, Guang’ai, and Xiaoqing Yue. "Dual Lie Bialgebra Structures of Twisted Schrödinger-Virasoro Type." Algebra Colloquium 25, no. 04 (December 2018): 627–52. http://dx.doi.org/10.1142/s1005386718000445.

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In this paper, the structures of dual Lie bialgebras of twisted Schrödinger-Virasoro type are investigated. By studying the maximal good subspaces, we determine the dual Lie coalgebras of the twisted Schrödinger-Virasoro algebras. Then based on this, we construct the dual Lie bialgebra structures of this type. As by-products, four new infinite dimensional Lie algebras are obtained.

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2

Su, Yihong, and Xue Chen. "Lie Bialgebras on the Rank Two Heisenberg–Virasoro Algebra." Mathematics 11, no. 4 (February 17, 2023): 1030. http://dx.doi.org/10.3390/math11041030.

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The rank two Heisenberg–Virasoro algebra can be viewed as a generalization of the twisted Heisenberg–Virasoro algebra. Lie bialgebras play an important role in searching for solutions of quantum Yang–Baxter equations. It is interesting to study the Lie bialgebra structures on the rank two Heisenberg–Virasoro algebra. Since the Lie brackets of rank two Heisenberg–Virasoro algebra are different from that of the twisted Heisenberg–Virasoro algebra and Virasoro-like algebras, and there are inner derivations (from itself to its tensor space) which are hidden more deeply in its interior algebraic structure, some new techniques and strategies are employed in this paper. It is proved that every Lie bialgebra structure on the rank two Heisenberg–Virasoro algebra is triangular coboundary.

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3

Fang, Xiao-Li, and Tae-Hwa Kim. "(𝜃,ω)-Twisted Radford’s Hom-biproduct and ϖ-Yetter–Drinfeld modules for Hom-Hopf algebras." Journal of Algebra and Its Applications 19, no. 03 (March 2020): 2050046. http://dx.doi.org/10.1142/s0219498820500462.

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To unify different definitions of smash Hom-products in a Hom-bialgebra [Formula: see text], we firstly introduce the notion of [Formula: see text]-twisted smash Hom-product [Formula: see text]. Secondly, we find necessary and sufficient conditions for the twisted smash Hom-product [Formula: see text] and the twisted smash Hom-coproduct [Formula: see text] to afford a Hom-bialgebra, which generalize the well-known Radford’s biproduct and the Hom-biproduct obtained in [H. Li and T. Ma, A construction of the Hom-Yetter–Drinfeld category, Colloq. Math. 137 (2014) 43–65]. Furthermore, we introduce the notion of the category of [Formula: see text]-Yetter-Drinfeld modules which unifies the ones of Hom-Yetter Drinfeld category appeared in [H. Li and T. Ma, A construction of the Hom-Yetter–Drinfeld category, Colloq. Math. 137 (2014) 43–65] and [A. Makhlouf and F. Panaite, Twisting operators, twisted tensor products and smash products for Hom-associative algebras, J. Math. Glasgow 513–538 (2016) 58]. Finally, we prove that the [Formula: see text]-twisted Radford’s Hom-biproduct [Formula: see text] is a Hom-bialgebra if and only if [Formula: see text] is a Hom-bialgebra in the category of [Formula: see text]-Yetter–Drinfeld modules [Formula: see text], generalizing the well-known Majid’s conclusion.

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4

Ma, Tianshui, Linlin Liu, and Shaoxian Xu. "Twisted tensor biproduct monoidal Hom–Hopf algebras." Asian-European Journal of Mathematics 10, no. 01 (March 2017): 1750011. http://dx.doi.org/10.1142/s1793557117500115.

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Let [Formula: see text] be a monoidal Hom-bialgebra, [Formula: see text] a monoidal Hom-algebra and a monoidal Hom-coalgebra. Let [Formula: see text] and [Formula: see text] be two linear maps. First, we construct the [Formula: see text]-smash product monoidal Hom-algebra [Formula: see text] and [Formula: see text]-smash coproduct monoidal Hom-coalgebra [Formula: see text]. Second, the necessary and sufficient conditions for [Formula: see text] and [Formula: see text] to be a monoidal Hom-bialgebra are obtained, which generalizes the results in [8, 11]. Lastly, we give some examples and applications.

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5

Fa, Huanxia, Junbo Li, and Bin Xin. "Lie Super-bialgebra Structures on the Centerless Twisted N=2 Super-conformal Algebra." Algebra Colloquium 18, no. 03 (September 2011): 361–72. http://dx.doi.org/10.1142/s1005386711000253.

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6

Fa, Huanxia, Meijun Li, and Junbo Li. "The deformed twisted Heisenberg–Virasoro type Lie bialgebra." Communications in Algebra 48, no. 6 (February 9, 2020): 2713–22. http://dx.doi.org/10.1080/00927872.2020.1722824.

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7

Fa, Huanxia, Yanjie Li, and Junbo Li. "Schrödinger-Virasoro type Lie bialgebra: a twisted case." Frontiers of Mathematics in China 6, no. 4 (February 19, 2011): 641–57. http://dx.doi.org/10.1007/s11464-011-0105-1.

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8

Liu, Dong, Yufeng Pei, and Linsheng Zhu. "Lie bialgebra structures on the twisted Heisenberg–Virasoro algebra." Journal of Algebra 359 (June 2012): 35–48. http://dx.doi.org/10.1016/j.jalgebra.2012.03.009.

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9

Yang, Shilin, and Yongfeng Zhang. "Ore Extensions for the Sweedler’s Hopf Algebra H4." Mathematics 8, no. 8 (August 5, 2020): 1293. http://dx.doi.org/10.3390/math8081293.

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The aim of this paper is to classify all Hopf algebra structures on the quotient of Ore extensions H4[z;σ] of automorphism type for the Sweedler′s 4-dimensional Hopf algebra H4. Firstly, we calculate all equivalent classes of twisted homomorphisms (σ,J) for H4. Then we give the classification of all bialgebra (Hopf algebra) structures on the quotients of H4[z;σ] up to isomorphism.

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10

Liu, Ling, Abdenacer Makhlouf, Claudia Menini, and Florin Panaite. "-Rota–Baxter Operators, Infinitesimal Hom-bialgebras and the Associative (Bi)Hom-Yang–Baxter Equation." Canadian Mathematical Bulletin 62, no. 02 (January 7, 2019): 355–72. http://dx.doi.org/10.4153/cmb-2018-028-8.

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AbstractWe introduce the concept of a $\{\unicode[STIX]{x1D70E},\unicode[STIX]{x1D70F}\}$ -Rota–Baxter operator, as a twisted version of a Rota–Baxter operator of weight zero. We show how to obtain a certain $\{\unicode[STIX]{x1D70E},\unicode[STIX]{x1D70F}\}$ -Rota–Baxter operator from a solution of the associative (Bi)Hom-Yang–Baxter equation, and, in a compatible way, a Hom-pre-Lie algebra from an infinitesimal Hom-bialgebra.

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Dissertations / Theses on the topic "Twisted bialgebra"

1

Ayadi, Mohamed. "Propriétés algébriques et combinatoires des espaces topologiques finis." Electronic Thesis or Diss., Université Clermont Auvergne (2021-...), 2022. http://www.theses.fr/2022UCFAC106.

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