On one-sided primitivity of Banach algebras

Crabb, M. J., Duncan, J. and McGregor, C. M. (2010) On one-sided primitivity of Banach algebras. Proceedings of the Edinburgh Mathematical Society, 53(01), pp. 111-123. (doi: 10.1017/S0013091508000783)

Abstract

Let S be the semigroup With identity, generated by x and y, subject to y being invertible and yx = xy(2). We study two Banach algebra completions of the semigroup algebra. CS. Both completions are shown to be left-primitive and have separating families of irreducible infinite-dimensional right, modules. As an appendix, we offer an alternative proof that US is left-primitive but Hot right-primitive. We show further that. in contrast to the completions: every irreducible right module for US is finite dimensional and hence that US has a separating family of such modules.

• 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.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Proceedings of the Edinburgh Mathematical Society
• ISSN: 0013-0915