Crossed Extensions of Lie Algebras

被引：0

作者：

Das, Apurba ^{[1
]}

机构：

[1] Indian Inst Technol, Dept Math & Stat, Kanpur, Uttar Pradesh, India

来源：

JOURNAL OF LIE THEORY | 2022年 / 32卷 / 02期

关键词：

Lie algebras; Chevalley-Eilenberg cohomology; crossed modules; crossed extensions; COHOMOLOGY; MODULES;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is known that Hochschild cohomology groups are represented by crossed extensions of associative algebras. In this paper, we introduce crossed n-fold extensions of a Lie algebra g by a module M, for n >= 2. We show that such extensions represent elements in the (n + 1)-th Chevalley-Eilenberg cohomology group H-CE(n+1)(g, M).

引用

页码：313 / 326

页数：14

共 50 条

[31] LIE DERIVATIONS OF DUAL EXTENSIONS OF ALGEBRAS
Li, Yanbo
Wei, Feng
COLLOQUIUM MATHEMATICUM, 2015, 141 (01) : 65 - 82
[32] EXTENSIONS OF REPRESENTATIONS OF LIE-ALGEBRAS
RYAN, JG
PACIFIC JOURNAL OF MATHEMATICS, 1987, 127 (01) : 173 - 186
[33] On Maximal Extensions of Nilpotent Lie Algebras
Gorbatsevich, V. V.
FUNCTIONAL ANALYSIS AND ITS APPLICATIONS, 2022, 56 (04) : 257 - 263
[34] Extensions of Hopf algebras and Lie bialgebras
Masuoka, A
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2000, 352 (08) : 3837 - 3879
[35] On Maximal Extensions of Nilpotent Lie Algebras
V. V. Gorbatsevich
Functional Analysis and Its Applications, 2022, 56 : 257 - 263
[36] Commutative central extensions of Lie algebras
Dzhumadil'daev, A. S.
Bakirova, A.
RUSSIAN MATHEMATICAL SURVEYS, 2008, 63 (04) : 776 - 777
[37] COHERENT PAIRS OF EXTENSIONS OF LIE ALGEBRAS
RAMABHAD.N
MATHEMATISCHE ZEITSCHRIFT, 1966, 93 (03) : 189 - &
[38] HNN-extensions of Lie algebras
Lichtman, AI
Shirvani, M
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1997, 125 (12) : 3501 - 3508
[39] Crossed product algebras defined by separable extensions
Lundström, P
JOURNAL OF ALGEBRA, 2005, 283 (02) : 723 - 737
[40] Crossed Modules for Lie 2-Algebras
Honglei Lang
Zhangju Liu
Applied Categorical Structures, 2016, 24 : 53 - 78

← 1 2 3 4 5 →