A characterization of *-minimal algebras with involution.
type: Item
instance of: scholarly article
title: A characterization of *-minimal algebras with involution.
zbMATH Open document ID: 1273.16018
author: Ernesto Spinelli
author: M. Onofrio Di Vincenzo
published in: Israel Journal of Mathematics
publication date: 2012-11-19T00:00:00Z
review text: Let \((A,*)\) be a *-PI algebra with involution over a field of characteristic zero and let \(c_m(A,*)\) denote its \(m\)-th *-codimension. \textit{A. Giambruno} and \textit{M. Zaicev}, [J. Algebra 222, No. 2, 471-484 (1999; Zbl 0944.16023)], proved that, if \(A\) is finite dimensional, then there exists \(\lim_{m\to+\infty}\root m\of {c_m(A,*)}\), and it is an integer, which is called the *-exponent of \(A\). As a consequence of the presence of this invariant, in a natural manner [\textit{O. M. Di Vincenzo} and \textit{R. La Scala}, J. Algebra 317, No. 2, 642-657 (2007; Zbl 1138.16008)] the definition of *-minimal algebra was introduced. The authors characterize, up to *-PI equivalence, *-minimal algebras. Theorem. A finite-dimensional algebra with involution is *-minimal if and only if it is *-PI equivalent to a block triangular matrix algebra with involution, denoted by \(UT_*(A_1,\dots,A_n)\), where \((A_1,\dots,A_n)\) is a suitable \(n\)-tuple of *-simple algebras.
Mathematics Subject Classification ID: 16R10
Mathematics Subject Classification ID: 16R50
Mathematics Subject Classification ID: 16W10
zbMATH DE Number: 6108405
zbMATH Keywords: PI-algebras
zbMATH Keywords: *-varieties
zbMATH Keywords: codimension sequences
zbMATH Keywords: involutions
reviewed by: Victor Petrogradsky
MaRDI profile type: Publication
full work available at URL: s11856-011-0144-z
OpenAlex ID: W2098366345
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DOI: 10.1007/S11856-011-0144-Z
description: scientific article; zbMATH DE number 6108405