Trace forms for structurable algebras
type: Item
instance of: scholarly article
title: Trace forms for structurable algebras
zbMATH Open document ID: 0672.17001
DOI: 10.1016/0021-8693(89)90085-9
published in: Journal of Algebra
publication date: 1989-01-01T00:00:00Z
review text: The authors investigate trace forms on a finite-dimensional structurable algebra \((A,^-)\) over a field of characteristic 0. A Lie algebra \(K(A,^-)\) corresponds to the structurable algebra \((A,^-)\) by a generalization of the Kantor-Tits-Koecher construction. Two trace forms are considered in the paper. The first is the symmetric bilinear form \(<x,y>=tr(L_{x\bar y+y\bar x})\) and the second is a trace form f(x,y) which is obtained by restricting the Killing form of \(K(A,^-)\) on \((A,^-).\) The authors establish that the trace form f is an invariant form. The radical of \((A,^-)\) is the radical of the form f and coincides with the radical of the form \(<, >\). Some known structure results on semisimple and radical algebras are reproved using the trace forms. Results on Hermitian idempotents are obtained, too.
Mathematics Subject Classification ID: 17A30
Mathematics Subject Classification ID: 17B60
zbMATH DE Number: 4099524
zbMATH Keywords: involution
zbMATH Keywords: associated Lie algebra
zbMATH Keywords: trace forms
zbMATH Keywords: structurable algebra
zbMATH Keywords: invariant form
zbMATH Keywords: radical
zbMATH Keywords: radical algebras
zbMATH Keywords: Hermitian idempotents
author: Bruce N. Allison
author: Schafer, R. D.
MaRDI profile type: Publication
full work available at URL: 0021-8693(89)90085-9
OpenAlex ID: W1968814535
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description: scientific article; zbMATH DE number 4099524