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Transactions of the American Mathematical Society
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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DOI: http://dx.doi.org/10.1090/S0002-9947-1976-0397310-4
PII: S 0002-9947(1976)0397310-4
Keywords: Inverse semigroup, $ {l^1}$-algebra of a semigroup, star representation
Article copyright: © Copyright 1976 American Mathematical Society