Restricted Lie algebras with bounded cohomology and related classes of algebras
type: Item
instance of: scholarly article
title: Restricted Lie algebras with bounded cohomology and related classes of algebras
zbMATH Open document ID: 0756.17008
DOI: 10.1007/BF02567657
author: Jörg Feldvoss
author: Helmut Strade
published in: Manuscripta Mathematica
publication date: 1992-09-27T00:00:00Z
full work available at URL: https://eudml.org/doc/155682
review text: The finite-dimensional Lie \(p\)-algebras \(L\) with bounded Hochschild cohomology (i.e. \(\dim H^ n_ *(L,M)<b(L,M)\) for every \(n\geq 0\)) are investigated. The equivalence of the following properties is stated: 1) \(L\) is special, 2) \(L\) is of finite module type, 3) \(L\) is of bounded module type, 4) \(L\) has periodic cohomology, 5) \(L\) has bounded cohomology. The structure of such algebras and their indecomposable \(p\)-representations are determined. In particular, all the Lie \(p\)-algebras of finite representation type are described.
Mathematics Subject Classification ID: 17B50
Mathematics Subject Classification ID: 17B56
zbMATH DE Number: 60086
zbMATH Keywords: restricted Lie algebras
zbMATH Keywords: Lie \(p\)-algebras
zbMATH Keywords: bounded Hochschild cohomology
zbMATH Keywords: indecomposable \(p\)-representations
zbMATH Keywords: finite representation type
reviewed by: Michael Kuznetsov
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 60086