Representations of the 𝑙¹-algebra of an inverse semigroup

Barnes, Bruce A.

doi:10.1090/S0002-9947-1976-0397310-4

Representations of the $l^{1}$-algebra of an inverse semigroup
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Trans. Amer. Math. Soc. 218 (1976), 361-396 Request permission

Abstract:

In this paper the star representations on Hilbert space of the ${l^1}$-algebra of an inverse semigroup are studied. It is shown that the set of all irreducible star representations form a separating family for the ${l^1}$-algebra. Then specific examples of star representations are constructed, and some theory of star representations is developed for the ${l^1}$-algebra of a number of the most important examples of inverse semigroups.

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