Second cohomology of generalized Cartan type \(H\) Lie algebras in characteristic 0
type: Item
instance of: scholarly article
title: Second cohomology of generalized Cartan type \(H\) Lie algebras in characteristic 0
zbMATH Open document ID: 0908.17014
author: Yuting Jia
published in: Journal of Algebra
publication date: 1999-03-14T00:00:00Z
review text: The author determines the second cohomology group \(H^2(L,F)\) of the generalized Cartan type \(H\) Lie algebras \(L=:L(A, \delta,\phi)\) under the condition that \(L\) is simple, where \(F\) is a field of characteristic 0 . Let \(M\) be the \(F\)-vector space consisting of all additive maps \(\mu: A \rightarrow F\) such that \(\mu(\delta_1)=\cdots =\mu(\delta_n)\), and \(\mu(\delta_1)=0\) if \(\phi_0 \neq 0\). His main result is as follows: Theorem 2.1: Let \(L=:L(A, \delta, \phi)\) be a generalized Cartan type \(H\) Lie algebra. Then \(H^2(L, F)\) is spanned by the cohomology classes \([\psi_1], [\psi_{2,i}]\), \([\psi_{3,i}]\) and \([\psi_{4,\mu}]\) for all \(i\in I\backslash \{0\}\) and all \(\mu \in M\).
reviewed by: Ye Jiachen
Mathematics Subject Classification ID: 17B56
zbMATH DE Number: 1218699
zbMATH Keywords: Lie algebra of Cartan type
zbMATH Keywords: second cohomology group
MaRDI profile type: Publication
full work available at URL: jabr.1997.7347
OpenAlex ID: W1982948908
cites work: Generalized Poisson brackets and Lie algebras of type \(H\) in characteristic 0
cites work: Q4890829
cites work: New simple infinite-dimensional Lie algebras of characteristic 0
cites work: New Simple Lie Algebras of Prime Characteristic
DOI: 10.1006/JABR.1997.7347
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description: scientific article; zbMATH DE number 1218699