Equivariant one-parameter deformations of Lie triple systems
type: Item
instance of: scholarly article
title: Equivariant one-parameter deformations of Lie triple systems
zbMATH Open document ID: 1461.17006
author: Yanyan Li
published in: Journal of Algebra
publication date: 2020-12-14T00:00:00Z
full work available at URL: https://arxiv.org/abs/2006.04526
review text: Lie triple systems were first noted by E. Cartan in his studies on totally geodesic submanifolds of Lie groups and on symmetric spaces. Lie triple systems were studied from the algebraic point of view by \textit{N. Jacobson} [Trans. Am. Math. Soc. 70, 509--530 (1951; Zbl 0044.02503)] and \textit{W. G. Lister} [Trans. Am. Math. Soc. 72, 217--242 (1952; Zbl 0046.03404)]. The deformation is a tool to study a mathematical object by deforming it into a family of the same kind of objects depending on a certain parameter. Algebraic deformation theory was introduced by \textit{M. Gerstenhaber} [Ann. Math. (2) 84, 1--19 (1966; Zbl 0147.28903)] for rings and algebras. The deformation theory for Lie triple systems is introduced by \textit{F. Kubo} and \textit{Y. Taniguchi} [J. Algebra 278, No. 1, 242--250 (2004; Zbl 1065.17010)]. In this article, the authors introduced equivariant formal deformation theory of Lie triple systems. They introduced an equivariant deformation cohomology of Lie triple systems and using this they studied the equivariant formal deformation theory of Lie triple systems.
Mathematics Subject Classification ID: 17A40
Mathematics Subject Classification ID: 16S80
Mathematics Subject Classification ID: 13D10
Mathematics Subject Classification ID: 13D03
Mathematics Subject Classification ID: 14D15
Mathematics Subject Classification ID: 16E40
Mathematics Subject Classification ID: 55N91
zbMATH DE Number: 7285345
zbMATH Keywords: Lie triple system
zbMATH Keywords: group actions
zbMATH Keywords: Yamaguti cohomology
zbMATH Keywords: equivariant formal deformations
zbMATH Keywords: equivariant cohomology
reviewed by: Shuangjian Guo
MaRDI profile type: Publication
OpenAlex ID: W3032909759
Wikidata QID: Q115350426
arXiv ID: 2006.04526
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DOI: 10.1016/J.JALGEBRA.2020.10.015
description: scientific article