Representation theory of the Witt algebra
type: Item
instance of: scholarly article
title: Representation theory of the Witt algebra
zbMATH Open document ID: 0913.17009
author: Jörg Feldvoss
author: Daniel K. Nakano
published in: Journal of Algebra
publication date: 1999-01-22T00:00:00Z
review text: For the smallest nonclassical restricted Lie algebra \(L=W(1:1)\) the representation and cohomology theory is studied. Let \(\chi \) be a linear function on \(L\) and \(u(L, \chi)\) a \(\chi \)-reduced enveloping algebra, i.e. \(u(L, \chi)=U(L)/J\) where \(J\) is the ideal of \(U(L)\) generated by \(x^p-x^{[p]}-\chi (x)^p1, x\in L.\) The dimensions of the projective indecomposable \(u(L, \chi)\)-modules and mutiplicities of their composition factors are determined. The support varieties and complexities of simple \(u(L, \chi)\)-modules are computed. The orbits of the characters \(\chi \) under the action of the automorphism group are described.
Mathematics Subject Classification ID: 17B50
Mathematics Subject Classification ID: 17B56
Mathematics Subject Classification ID: 17B10
zbMATH DE Number: 1200007
zbMATH Keywords: modular Lie algebra
zbMATH Keywords: representation
zbMATH Keywords: cohomology
zbMATH Keywords: support variety
zbMATH Keywords: complexity
reviewed by: Michael Kuznetsov
MaRDI profile type: Publication
full work available at URL: jabr.1997.7343
OpenAlex ID: W1998998869
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DOI: 10.1006/JABR.1997.7343
description: scientific article; zbMATH DE number 1200007