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Rings related to completely 0-simple semigroups

Published online by Cambridge University Press:  09 April 2009

D. B. McAlister
D. B. McAlister
Affiliation:
Department of Pure Mathematics Queen's University, Belfast
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A.H. Clifford ([2], [3]) has shown that all finite dimensional irreducible representations of a completely 0-simple semigroup can be obtained as extensions of those of its maximal subgroups. Lallement and Petrich, [7], have given an alternative method for constructing the irreducible representations of a finite 0-simple semigroup from its Schutzenberger representation ([13]). Using the form which they obtain for the irreducible representations of a finite 0-simple semigroup S = M0(G; m, n; P), Lallement and Petrich show that where M is the Munn algebra isomorphic to the (contracted) algebra Φ(S) of S over Φ.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 12 , Issue 3 , August 1971 , pp. 257 - 274
Copyright
Copyright © Australian Mathematical Society 1971

References

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