Hostname: page-component-6d856f89d9-nr6nt Total loading time: 0 Render date: 2024-07-16T04:06:16.490Z Has data issue: false hasContentIssue false
  • English
  • Français

Involutions on finite-dimensional algebras over real closed fields

Part of: Rings and algebras with additional structure

Published online by Cambridge University Press:  09 April 2009

W. D. Munn
W. D. Munn
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow G12 8QW, Scotland, UK e-mail: [email protected]
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 following conditions on a finite-dimensional algebra A over a real closed field or an algebraically closed field of characteristic zero are equivalent: (i) A admits a special involution, in the sense of Easdown and Munn, (ii) A admits a proper involution, (iii) A is semisimple.

MSC classification

Secondary: 16W10: Rings with involution; Lie, Jordan and other nonassociative structures
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 77 , Issue 1 , August 2004 , pp. 123 - 128
Copyright
Copyright © Australian Mathematical Society 2004

References

[1]Crabb, M. J., McGregor, C. M., Munn, W. D. and Wassermann, S., ‘On the algebra of a free monoid’, Proc. Roy. Soc. Edinburgh Sect. 126 (1996), 939–945.Google Scholar
[2]Easdown, D. and Munn, W. D., ‘On semigroups with involution’, Bull. Austral. Math. Soc. 48 (1993), 103–110.CrossRefGoogle Scholar
[3]Easdown, D. and Munn, W. D., ‘Trace functions on inverse semigroup algebras’, Bull. Austral. Math. Soc. 52 (1995), 359–372.CrossRefGoogle Scholar
[4]Munn, W. D., ‘Special involutions’, in: Semigroup theory and its applications (New Orleans, LA, 1994) (eds. Hofmann, K. H. and Mislove, M. W.), London Math. Soc. Lecture Note Ser. 231 (Cambridge University Press, Cambridge, 1996) pp. 157–165.Google Scholar
[5]Van der Waerden, B. L., Modern algebra, English edition (Ungar, New York, 1949 (Vol. I) and 1950 (Vol. II)).Google Scholar