Simple algebras of hermitian operators
type: Item
instance of: scholarly article
title: Simple algebras of hermitian operators
zbMATH Open document ID: 0853.17021
DOI: 10.1007/BF01194173
author: Xiarong Shen
author: J. D. H. Smith
published in: Archiv der Mathematik
publication date: 1997-01-09T00:00:00Z
review text: The paper is part of a continuing programme [cf. Arch. Math. 59, 327-333 (1992; Zbl 0739.17010); J. Pure Appl. Algebra 80, 177-195 (1992; Zbl 0758.17001); J. Algebra 160, 424-433 (1993; Zbl 0811.17024)] of classifying simple comtrans algebras. The main result shows that the space of hermitian matrices of a given size furnishes a simple comtrans algebra. Comtrans algebra structure on real spaces of hermitian operators was introduced initially [cf. Banach Cent. Publ. 28, 319-326 (1993; Zbl 0811.17025)] as part of a discussion of applications to quantum mechanics.
Mathematics Subject Classification ID: 17B60
Mathematics Subject Classification ID: 17B99
zbMATH DE Number: 937049
zbMATH Keywords: Jordan algebra
zbMATH Keywords: Lie algebra
zbMATH Keywords: simple comtrans algebras
zbMATH Keywords: hermitian matrices
MaRDI profile type: Publication
cites work: Q5543320
cites work: Simple multilinear algebras, rectangular matrices and Lie algebras
cites work: Representation theory of comtrans algebras
cites work: Multilinear algebras and Lie's theorem for formal \(n\)-loops
cites work: Q4273439
description: scientific article; zbMATH DE number 937049