Constructions of Lie algebras and their modules
type: Item
instance of: scholarly article
title: Constructions of Lie algebras and their modules
zbMATH Open document ID: 0633.17005
author: George B. Seligman
published in: Lecture Notes in Mathematics
publication date: 1993-06-05T00:00:00Z
review text: Let \({\mathfrak g}\) be a central simple Lie algebra over a field of characteristic zero. In these notes the author is interested in constructing all irreducible \({\mathfrak g}\)-modules of finite dimension in terms related to structural descriptions of \({\mathfrak g}\). It is his stated objective to demonstrate the constructions of the irreducible modules in the isotropic cases with non-reduced root systems, and in all anisotropic cases where \({\mathfrak g}\) is neither exceptional nor an exceptional form of \(D_ 4.\) For purposes of motivation and illustration he begins by treating algebras ``of inner type A'' before giving a general discussion of the basic principles of the program to be followed. He then deals with the remaining classical algebras with the generalized even Clifford algebras playing a central part in the construction of the modules. The treatment of exceptional algebras begins by developing constructions of exceptional algebras from quadratic forms in low dimensions and later moves on to constructions of ``super-exceptional'' Lie algebras using the approach of Kantor and Allison. A few additional related topics are briefly discussed in a short final chapter.
Mathematics Subject Classification ID: 17B10
Mathematics Subject Classification ID: 17B20
Mathematics Subject Classification ID: 17-02
Mathematics Subject Classification ID: 15A66
Mathematics Subject Classification ID: 17C40
Mathematics Subject Classification ID: 16W10
zbMATH DE Number: 192829
zbMATH Keywords: central simple Lie algebra
zbMATH Keywords: characteristic zero
zbMATH Keywords: irreducible modules
zbMATH Keywords: isotropic cases with non-reduced root systems
zbMATH Keywords: anisotropic cases
zbMATH Keywords: generalized even Clifford algebras
zbMATH Keywords: exceptional algebras
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bfb0079295
OpenAlex ID: W643561542
DOI: 10.1007/BFB0079295
description: scientific article; zbMATH DE number 192829