Vol. 19, No. 2, 1966

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On representations of certain semigroups

Michael Friedberg

Vol. 19 (1966), No. 2, 269–274

A theory of representations for compact semigroups has been lacking due in large part to the absence of a translation-invariant carrying measure that exists for compact groups. The object in this paper is to show that for a compact, group-extremal affine semigroup there is a sufficient system of representations by linear operators on finite-dimensional complex linear spaces; in the abelian case, a sufficient system of affine semicharacters is obtained. As a result, a compact group-extremal affine semigroup is the inverse limit of compact, finite-dimensional, group-extremal affine semigroups.

Mathematical Subject Classification
Primary: 22.05
Received: 2 August 1965
Published: 1 November 1966
Michael Friedberg