Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-13T10:46:59.346Z Has data issue: false hasContentIssue false
  • English
  • Français

A property of the complex semigroup algebra of a free monoid

Part of: Rings and algebras arising under various constructions Semigroups

Published online by Cambridge University Press:  09 April 2009

M. J. Crabb ,
C. M. McGregor  and
W. D. Munn
M. J. Crabb
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow G12 8QW, Scotland, UK, e-mail: mjc@maths.gla.ac.uk, cmm@maths.gla.ac.uk, wdm@maths.gla.ac.uk
C. M. McGregor
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow G12 8QW, Scotland, UK, e-mail: mjc@maths.gla.ac.uk, cmm@maths.gla.ac.uk, wdm@maths.gla.ac.uk
W. D. Munn
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow G12 8QW, Scotland, UK, e-mail: mjc@maths.gla.ac.uk, cmm@maths.gla.ac.uk, wdm@maths.gla.ac.uk
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

It is shown that the complex semigroup algebra of a free monoid of rank at least two is *-primitive, where * denotes the involution on the algebra induced by word-reversal on the monoid.

MSC classification

Secondary: 16S10: Rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.) 16S36: Ordinary and skew polynomial rings and semigroup rings 20M25: Semigroup rings, multiplicative semigroups of rings
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 81 , Issue 1 , August 2006 , pp. 97 - 104
Copyright
Copyright © Australian Mathematical Society 2006

References

[1]Chaudry, M. A., Crabb, M. J. and McGregor, C. M., ‘The primitivity of semigroup algebras of free products’, Semigroup Forum 54 (1997), 221–229.CrossRefGoogle Scholar
[2]Crabb, M. J. and McGregor, C. M., ‘Faithful irreducible *-representations for group algebras of free products’, Proc. Edinburgh Math. Soc. (2) 42 (1999), 559–574.Google Scholar
[3]Crabb, M. J., McGregor, C. M., Munn, W. D. and Wassermann, S., ‘On the algebra of a free monoid’, Proc. Roy. Soc. Edinburgh Sect. A 126 (1996), 939–945.Google Scholar
[4]Formanek, E., ‘Group rings of free products are primitive’, J. Algebra 26 (1973), 508–511.Google Scholar
[5]Irving, R., ‘Irreducible *-representations of some group rings and associated Banach *-algebras’, J. Funct. Anal. 39 (1980), 149–161.Google Scholar
[6]McGregor, C. M., ‘On the primitivity of the group ring of a free group’, Bull. London. Math. Soc. 8 (1976), 294–298.CrossRefGoogle Scholar
[7]McGregor, C. M., ‘A representation for l1 (S)’, Bull. London Math. Soc. 8 (1976), 156–160.Google Scholar
[8]Passman, D. S., The algebraic theory of group rings (Wiley-Interscience, New York, 1977).Google Scholar