3-HOM-LIE SUPERBIALGEBRAS AND 3-HOM-LIE CLASSICAL YANG-BAXTER EQUATIONS

被引：0

作者：

Bartouli, Issam ^{[1
]}

Basdouri, Imed ^{[2
]}

Chaabane, Gaith ^{[3
]}

Fadous, Mohamed ^{[3
]}

Lerbet, Jean

机构：

[1] Univ Evry Val d EssonneI, Lab Math & Modelisat Evry, UMR 8071, IBGBI, IBGBI 23 Bd France, F-91037 Evry, France

[2] Univ Gafsa, Fac Sci Gafsa, Gafsa 2112, Tunisia

[3] Univ Sfax, Fac Sci Sfax, BP 1171, Sfax 3038, Tunisia

来源：

COMMUNICATIONS OF THE KOREAN MATHEMATICAL SOCIETY | 2024年 / 39卷 / 01期

关键词：

Bialgebras; Yang-Baxter equations; Lie bialgebras; Lie coalge- bras; Hom-Lie and related algebras; representation; central extension; double extension; 3-LIE ALGEBRAS; BIALGEBRAS; REPRESENTATIONS; COHOMOLOGY;

D O I：

10.4134/CKMS.c230055

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

3 -Lie algebras are in close relationships with many fields. In this paper we are concerned with the study of 3-Hom-Lie super algebras, the concepts of 3-Hom-Lie coalgebras and how they make a 3-Hom-Lie superbialgebras, we study the structures of such categories of algebras and the relationships between each others. We study a super twisted 3ary version of the Yang -Baxter equation, called the super 3 -Lie classical Hom-Yang-Baxter equation (3 -Lie CHYBE), which is a general form of 3 -Lie classical Yang -Baxter equation and prove that the superbialgebras induced by the solutions of the super 3 -Lie CHYBE induce the cob oundary local cocycle 3-Hom-Lie superbialgebras.

引用

页码：11 / 30

页数：20

共 31 条

[21] Relative Rota-Baxter operators on Hom-Lie triple systems [J].

Li, Yizheng ;

Wang, Dingguo .

COMMUNICATIONS IN ALGEBRA, 2024, 52 (03) :1163-1178

[22] Cohomology and Deformations of 3-Dimensional Heisenberg Hom-Lie Superalgebras [J].

Zhu, Junxia ;

Chen, Liangyun .

CZECHOSLOVAK MATHEMATICAL JOURNAL, 2021, 71 (02) :335-350

[23] Cohomology and Deformations of 3-Dimensional Heisenberg Hom-Lie Superalgebras [J].

Junxia Zhu ;

Liangyun Chen .

Czechoslovak Mathematical Journal, 2021, 71 :335-350

[24] Folded and contracted solutions of coupled classical dynamical Yang-Baxter and reflection equations [J].

Stokman, Jasper, V .

INDAGATIONES MATHEMATICAE-NEW SERIES, 2021, 32 (06) :1372-1411

[25] Double product integrals and enriquez quantisation of Lie bialgebras II:: The quantum Yang-Baxter equation [J].

Hudson, RL ;

Pulmannová, S .

LETTERS IN MATHEMATICAL PHYSICS, 2005, 72 (03) :211-224

[26] Twisting O-operators by (2,3)-cocycle of Hom-Lie-Yamaguti algebras with representations [J].

Mabrouk, Sami ;

Silvestrov, Sergei ;

Zouaidi, Fatma .

JOURNAL OF GEOMETRY AND PHYSICS, 2025, 216

[27] Matching Hom-Setting of Rota-Baxter Algebras, Dendriform Algebras, and Pre-Lie Algebras [J].

Chen, Dan ;

Peng, Xiao-Song ;

Zargeh, Chia ;

Zhang, Yi .

ADVANCES IN MATHEMATICAL PHYSICS, 2020, 2020

[28] Lie 3-algebras and deformations of relative Rota-Baxter operators on 3-Lie algebras [J].

Tang, Rong ;

Hou, Shuai ;

Sheng, Yunhe .

JOURNAL OF ALGEBRA, 2021, 567 :37-62

[29] 3-post-Lie algebras and relative Rota-Baxter operators of nonzero weight on 3-Lie algebras [J].

Hou, Shuai ;

Sheng, Yunhe ;

Zhou, Yanqiu .

JOURNAL OF ALGEBRA, 2023, 615 :103-129

[30] CLASSIFICATION OF ROTA-BAXTER OPERATORS ON THE 3-LIE ALGEBRA A4 [J].

Kang, Chuangchuang ;

Bai, Ruipu ;

Hou, Shuai .

MATHEMATICAL REPORTS, 2022, 24 (04) :645-672

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