Filtering bases, cohomology of infinite-dimensional Lie algebras, and Laplace operators
type: Item
instance of: scholarly article
title: Filtering bases, cohomology of infinite-dimensional Lie algebras, and Laplace operators
zbMATH Open document ID: 0593.17010
DOI: 10.1007/BF01077290
author: F. V. Vaĭnshteĭn
publication date: 1985-01-01T00:00:00Z
review text: Let \(L_ k(1)=L_ k\) be the Lie algebra of polynomial vector fields on the line over the field of rational numbers, having trivial \(k\)-jet at the origin. The basic result of the paper is the construction of a special filtered basis in the exterior complex of \(L_ k\). This construction gives another proof of L. V. Goncharova's theorem on the cohomology of \(L_ k\) [see \textit{L. V. Goncharova}, ibid. 7, No. 2, 6--14 (1973; Zbl 0284.17006), No. 3, 33--44 (1973; Zbl 0289.57026)]. Such a special filtered basis is also constructed for the simplest Kac-Moody algebra of affine type.
reviewed by: Alice Fialowski
Mathematics Subject Classification ID: 17B56
Mathematics Subject Classification ID: 17B66
Mathematics Subject Classification ID: 17B67
zbMATH DE Number: 3953020
zbMATH Keywords: Laplace operator
zbMATH Keywords: affine Kac-Moody algebra
zbMATH Keywords: Lie algebra of polynomial vector fields
zbMATH Keywords: filtered basis
zbMATH Keywords: L. V. Goncharova's theorem
zbMATH Keywords: cohomology
MaRDI profile type: Publication
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published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 3953020