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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Representations of the $ l\sp{1}$-algebra of an inverse semigroup

Author: Bruce A. Barnes
Journal: Trans. Amer. Math. Soc. 218 (1976), 361-396
MSC: Primary 43A20; Secondary 43A65
MathSciNet review: 0397310
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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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Keywords: Inverse semigroup, $ {l^1}$-algebra of a semigroup, star representation
Article copyright: © Copyright 1976 American Mathematical Society

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