A periodisation of semisimple Lie algebras
type: Item
instance of: scholarly article
title: A periodisation of semisimple Lie algebras
zbMATH Open document ID: 0995.17009
author: Anna Larsson
published in: Homology, Homotopy and Applications
publication date: 2002-08-01T00:00:00Z
full work available at URL: https://eudml.org/doc/49421
full work available at URL: volume4-2-2.htm
review text: A periodisation of a Lie algebra \(L\) over a field \(K\) is a Lie algebra \(L\otimes tK[t]\) with a Lie bracket defined naturally by tensor components. (So, roughly speaking, periodisation is a positively-graded Lie algebra with an underlying Lie algebra in each degree.) In this interesting paper the author proves that a periodisation of a semisimple Lie algebra over an algebraically closed field of characteristic \(0\) without direct summands isomorphic to \(sl(2)\) possesses a presentation with only quadratic relations. Such a presentation is explicitly constructed in terms of a Chevalley basis of an underlying Lie algebra. The author promises to handle the analogous problem for Lie superalgebras in a subsequent paper. The motivation of study of presentations of periodisations of Lie superalgebras stems from the work of \textit{C. Löfwall} and \textit{J.-E. Roos} about some amazing Hopf algebras [Adv. Math. 130, 161-200 (1997; Zbl 0903.17012)].
reviewed by: Pasha Zusmanovich
Mathematics Subject Classification ID: 17B70
Mathematics Subject Classification ID: 17B20
zbMATH DE Number: 1770080
zbMATH Keywords: graded Lie algebras
zbMATH Keywords: Chevalley basis
zbMATH Keywords: current algebras
zbMATH Keywords: presentations
zbMATH Keywords: periodisation
MaRDI profile type: Publication
DOI: 10.4310/HHA.2002.V4.N2.A16
description: scientific article; zbMATH DE number 1770080