Computation of cohomology groups of the Lie algebras of type \(B_n\) and \(C_n\)
type: Item
instance of: scholarly article
title: Computation of cohomology groups of the Lie algebras of type \(B_n\) and \(C_n\)
zbMATH Open document ID: 1205.17001
DOI: 10.3103/S1066369X0908009X
author: D. V. Reshetnikov
published in: Russian Mathematics
publication date: 2009-11-13T00:00:00Z
review text: This short note announces the implementation of a computer package to compute the second cohomology group of classical Lie algebras of type \(B_n\), \(C_n\) over a field of characteristic \(p=2\). For the orthogonal case, it is shown that for ranks \(3\leq n\leq 7\) the cohomology group \(H^2(L,L)\) vanishes, up to the case of \(n=4\), which is of dimension \(16\). The basis of cocycles is given. For the \(C_n\) case, it is shown that for ranks \(3\leq n\leq 8\) the cohomology group has dimension \(2n^2+5n-1\). This confirms previous examples in the literature indicating that the rigidity properties of classical algebras do not generally extend to positive characteristic.
Mathematics Subject Classification ID: 17-08
Mathematics Subject Classification ID: 17B56
Mathematics Subject Classification ID: 17B50
zbMATH DE Number: 5633033
zbMATH Keywords: cohomology group
zbMATH Keywords: classical Lie algebra
zbMATH Keywords: local deformation
zbMATH Keywords: characteristic 2
reviewed by: Rutwig Campoamor Stursberg
MaRDI profile type: Publication
Wikidata QID: Q115223356
cites work: Q5638468
cites work: Deformations of classical Lie algebras of characteristic three
cites work: Deformations of classical Lie algebras
cites work: Deformations of the Lie algebra of type \(G_2\) of characteristic 3
full work available at URL: s1066369x0908009x
OpenAlex ID: W2088046668
description: scientific article; zbMATH DE number 5633033