The extremal algebra on two hermitians with square 1

Crabb, M.J., Duncan, J. and McGregor, C.M. (2002) The extremal algebra on two hermitians with square 1. Glasgow Mathematical Journal, 44(2), pp. 255-260. (doi: 10.1017/S0017089502020062)

Abstract

Let Ea(u,v) be the extremal algebra determined by two hermitians u and v with u² = v² = 1. We show that: Ea(u,v) = {f=gu:f,g ε C(T)}, where T is the unit circle; Ea(u,v) is C^*-equivelant to C^*(G), where G is the infinite dihedral group; most of the hermitian elements k od Ea(u,v) have the property that kⁿ is hermitian for all odd n but for no even n; any two hermitian words in G generate an isometric copy of Ea(u,v) in Ea(u,v).

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: McGregor, Dr Colin and Crabb, Dr Michael
• Authors: Crabb, M.J., Duncan, J., and McGregor, C.M.
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Glasgow Mathematical Journal
• Publisher: Cambridge University Press
• ISSN: 0017-0895
• ISSN (Online): 1469-509X
• Published Online: 25 July 2002
• Copyright Holders: Copyright © 2002 Glasgow Mathematical Journal Trust
• First Published: First published in Glasgow Mathematical Journal 44(2):255-260
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher