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A Class of Irreducible matrix representations of an Arbitrary Inverse Semigroup

Published online by Cambridge University Press:  18 May 2009

W. D. Munn
W. D. Munn
Affiliation:
The University Glasgow
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By a ‘representation’ we shall mean throughout a representation by n × n matrices with entries from an arbitrary field. Elsewhere [9] the author has introduced the concept of a principal representation of a semigroup S (see § 3 below for the definition) and has shown that if S satisfies the minimal condition on principal ideals then every irreducible representation is of this type. Moreover, if S satisfies the minimal conditions on both principal left and right ideals, which together imply the minimal condition on principal two-sided ideals [6, Theorem 4], the irreducible representations of S can ultimately be expressed explicitly in terms of group representations.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 5 , Issue 1 , January 1961 , pp. 41 - 48
Copyright
Copyright © Glasgow Mathematical Journal Trust 1961

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