Scalar products on Clifford modules and pseudo-\(H\)-type Lie algebras
type: Item
instance of: scholarly article
title: Scalar products on Clifford modules and pseudo-\(H\)-type Lie algebras
zbMATH Open document ID: 1027.17008
DOI: 10.1007/BF02505885
author: Paolo Ciatti
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 2003-09-24T00:00:00Z
review text: The author introduces the notion of pseudo-Heisenberg type Lie algebras, that is, Lie algebras that are two-step nilpotent equipped with a scalar product of signature \((p,q)\), plus a compatibility condition with the Lie algebra structure. It is shown that a \((p,q)\)-algebra structure exists on a vector space if and only if a corresponding representation for the Clifford algebra \(\mathcal C(p,q)\) is admissible. So the existence of pseudo-\(H\)-type algebras is reduced to the existence of admissible modules. The author then proceeds to construct such modules for all pairs \((p,q)\). Finally he studies the admissibility of an irreducible \(\mathcal C(p,q)\)-module.
reviewed by: Stefano Capparelli
Mathematics Subject Classification ID: 17B30
Mathematics Subject Classification ID: 22E25
Mathematics Subject Classification ID: 46C99
zbMATH DE Number: 1985419
zbMATH Keywords: Clifford modules
zbMATH Keywords: Heisenberg algebra
MaRDI profile type: Publication
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Wikidata QID: Q126093684
full work available at URL: https://doi.org/10.1007/bf02505885
OpenAlex ID: W2072187590
description: scientific article; zbMATH DE number 1985419