Involutionen zweiter Art in halbeinfachen Algebren. (Involutions of the second kind in semisimple algebras)
type: Item
instance of: scholarly article
title: Involutionen zweiter Art in halbeinfachen Algebren. (Involutions of the second kind in semisimple algebras)
zbMATH Open document ID: 0618.16011
author: Kurt Rosenbaum
author: Frank Neumann
published in: Beiträge zur Algebra und Geometrie
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/138372
review text: Let A be a finite-dimensional semismiple algebra over an algebraically closed field K. This article describes all involutions * of A that act non-trivially on K (called involutions of the second kind). If A is simple, \(A=M_ n(K)\) say, and \({}^-\) denotes the map that transforms all matrix entries via *, then * on A is given by \(x^*=c\bar x^ Tc^{-1}\) \((x\in A)\) for some ''\(\lambda\)-hermitian'' matrix C. A minor adjustment is needed in the general case.
Mathematics Subject Classification ID: 16W10
Mathematics Subject Classification ID: 16Kxx
Mathematics Subject Classification ID: 16P10
zbMATH DE Number: 4002303
zbMATH Keywords: finite-dimensional semismiple algebra
zbMATH Keywords: involutions
reviewed by: Martin Lorenz
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4002303