(Co)homology and crossed module for BiHom-associative algebras

被引：0
|
作者：
Huang, Danli [1 ]
Liu, Ling [1 ]
机构：
[1] Zhejiang Normal Univ, Sch Math Sci, Jinhua 321004, Peoples R China
来源：
JOURNAL OF ALGEBRA | 2024年 / 644卷
关键词：
BiHom-associative algebra; Hochschild cohomology; Cyclic homology; Crossed module; DEFORMATIONS; COHOMOLOGY;
D O I：
10.1016/j.jalgebra.2024.01.022
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
BiHom-associative algebras are generalized associative algebras with two multiplicative linear maps. In this paper, we give the Hochschild homology and cyclic homology structure of BiHom-associative algebras. Then, generalize the dual bimodule action to define the cyclic cohomology. Finally, we introduce the crossed modules of BiHom-associative algebras and show that the Hochschild cohomology of BiHomassociative algebra classifies crossed modules. (c) 2024 Elsevier Inc. All rights reserved.
引用
收藏
页码：835 / 864
页数：30
相关论文
共 50 条
  • [1] Cohoinology of BiHom-associative algebras
    Das, Apurba
    JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2022, 21 (01)
  • [2] BiHom-Associative Algebras, BiHom-Lie Algebras and BiHom-Bialgebras
    Graziani, Giacomo
    Makhlouf, Abdenacer
    Menini, Claudia
    Panaite, Florin
    SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, 2015, 11
  • [3] The cohomology and deformations of O-operators on BiHom-associative algebras
    Huang, Danli
    Liu, Ling
    Lu, Jiafeng
    JOURNAL OF ALGEBRA, 2025, 662 : 138 - 166
  • [4] ROTA-BAXTER OPERATORS ON BIHOM-ASSOCIATIVE ALGEBRAS AND RELATED STRUCTURES
    Liu, Ling
    Makhlouf, Abdenacer
    Menini, Claudia
    Panaite, Florin
    COLLOQUIUM MATHEMATICUM, 2020, 161 (02) : 263 - 294
  • [5] Rota-Baxter Operators and Loday-Type Algebras on the BiHom-Associative Conformal Algebras
    Asif, Sania
    Wang, Yao
    COMPLEX ANALYSIS AND OPERATOR THEORY, 2025, 19 (02)
  • [6] (Co)homology of compatible associative algebras
    Chtioui, Taoufik
    Das, Apurba
    Mabrouk, Sami
    COMMUNICATIONS IN ALGEBRA, 2024, 52 (02) : 582 - 603
  • [7] (Co)homology of crossed products by weak Hopf algebras
    Guccione, Jorge A.
    Guccione, Juan J.
    Valqui, Christian
    JOURNAL OF ALGEBRA, 2023, 622 : 30 - 68
  • [8] ON THE HOMOLOGY OF ASSOCIATIVE ALGEBRAS
    ANICK, DJ
    TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1986, 296 (02) : 641 - 659
  • [9] CO-HOMOLOGY FOR MODULES OVER ASSOCIATIVE ALGEBRAS
    TRUSHIN, DS
    JOURNAL OF ALGEBRA, 1978, 51 (02) : 550 - 561
  • [10] More about the (co)homology of groups and associative algebras
    Inassaridze, Hvedri
    HOMOLOGY HOMOTOPY AND APPLICATIONS, 2005, 7 (01) : 87 - 108
12345