An Allison-Kantor-Koecher-Tits construction for Lie \(H^*\)-algebras
type: Item
instance of: scholarly article
title: An Allison-Kantor-Koecher-Tits construction for Lie \(H^*\)-algebras
zbMATH Open document ID: 0839.17001
author: V. Pereyra
published in: Journal of Algebra
publication date: 1994-06-06T00:00:00Z
review text: The authors establish a correspondence between the class of (complex) structurable \(H^*\)-algebras [for the definition see the authors, J. Algebra 147, 19-62 (1992; Zbl 0749.17001)] with zero annihilator and the class of Lie \(H^*\)-algebras with zero annihilator. The construction providing this correspondence is a topological version of the Allison-Kantor construction for general structurable algebras (without an additional Hilbert space structure). Furthermore, it is proved that the lattices of closed ideals of a structurable \(H^*\)-algebra \((A, {}^-)\) and the associated Lie \(H^*\)-algebra \(K(A,{}^-)\) are isomorphic. It follows that \(K(A,{}^-)\) is topologically simple if and only if \((A,{}^-)\) is topologically simple as an algebra with involution. Also, it is shown that any topologically simple Lie \(H^*\)-algebra can be obtained as \(K(A,{}^-)\) for a suitable \((A,{}^-)\).
Mathematics Subject Classification ID: 17A30
Mathematics Subject Classification ID: 46K70
Mathematics Subject Classification ID: 17B70
zbMATH DE Number: 562442
zbMATH Keywords: structurable algebras
zbMATH Keywords: Tits-Kantor-Koecher construction
zbMATH Keywords: structurable \(H^*\)-algebras
zbMATH Keywords: zero annihilator
zbMATH Keywords: Lie \(H^*\)-algebras
zbMATH Keywords: Allison-Kantor construction
zbMATH Keywords: topologically simple Lie \(H^*\)-algebra
Wikidata QID: Q115396265
MaRDI profile type: Publication
full work available at URL: jabr.1994.1065
OpenAlex ID: W2015885048
DOI: 10.1006/JABR.1994.1065
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description: scientific article; zbMATH DE number 562442