The non-abelian tensor and exterior products of crossed modules of Lie superalgebras

被引：0

作者：

Taha, Tahereh Fakhr ^{[1
]}

Ladra, Manuel ^{[2
]}

Paez-Guillan, Pilar ^{[3
]}

机构：

[1] Shahid Beheshti Univ, Fac Math Sci, GC, Tehran, Iran

[2] Univ Santiago de Compostela, Inst Matemat, Dept Matemat, Santiago De Compostela 15782, Spain

[3] Univ Santiago de Compostela, Dept Matemat, Santiago De Compostela 15782, Spain

来源：

JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2022年 / 21卷 / 09期

关键词：

Lie superalgebra; crossed module; non-abelian tensor product; non-abelian exterior product; homology of crossed modules; semi-abelian category; HOMOLOGY;

D O I：

10.1142/S0219498822501699

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we introduce the notions of non-abelian tensor and exterior products of two ideal graded crossed submodules of a given crossed module of Lie superalgebras. We also study some of their basic properties and their connection with the second homology of crossed modules of Lie superalgebras.

引用

页数：22

共 37 条

[21] Crossed modules, non-abelian extensions of associative conformal algebras and wells exact sequences
Hou, Bo
Zhao, Jun
JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2024,
[22] On the Non-abelian Tensor Product of Groups
Moghaddam, Mohammad Reza R.
Mirzaei, Fateme
ALGEBRA COLLOQUIUM, 2011, 18 (03) : 429 - 436
[23] On some closure properties of the non-abelian tensor product
Donadze, G.
Ladra, M.
Thomas, V. Z.
JOURNAL OF ALGEBRA, 2017, 472 : 399 - 413
[24] On the finiteness of the non-abelian tensor product of groups
Bastos, Raimundo
Nakaoka, Irene N.
Rocco, Norai R.
JOURNAL OF ALGEBRA, 2025, 664 : 251 - 267
[25] UNIVERSAL CENTRAL EXTENSIONS AND NON-ABELIAN TENSOR PRODUCT OF HOM-LIE-RINEHART ALGEBRAS
Mandal, Ashis
Mishra, Satyendra Kumar
COLLOQUIUM MATHEMATICUM, 2021, 166 (01) : 23 - 52
[26] Tensor Products and Crossed Differential Graded Lie Algebras in the Category of Crossed Complexes
Igde, Elif
Yilmaz, Koray
SYMMETRY-BASEL, 2023, 15 (09):
[27] Non-abelian tensor product and circular orderability of groups ☆
Ivanov, Maxim
TOPOLOGY AND ITS APPLICATIONS, 2024, 358
[28] NON-ABELIAN HOMOLOGY OF HOM-LIE ALGEBRAS AND APPLICATIONS
Casas, J. M.
Khmaladze, E.
Rego, N. Pacheco
PROCEEDINGS OF A RAZMADZE MATHEMATICAL INSTITUTE, 2015, 167 : 99 - 106
[29] Non-abelian extensions of infinite-dimensional Lie groups
Neeb, Karl-Hermann
ANNALES DE L INSTITUT FOURIER, 2007, 57 (01) : 209 - 271
[30] The non-abelian tensor product and the second homology of Leibniz algebras
Hosseini, Seyedeh Narges
Edalatzadeh, Behrouz
Salemkar, Ali Reza
COMMUNICATIONS IN ALGEBRA, 2020, 48 (02) : 759 - 770

← 1 2 3 4 →