منابع مشابه
Inverse Semigroups and Combinatorial C*-algebras
We describe a special class of representations of an inverse semigroup S on Hilbert's space which we term tight. These representations are supported on a subset of the spectrum of the idempotent semilattice of S, called the tight spectrum, which is in turn shown to be precisely the closure of the space of ultra-filters, once filters are identified with semicharacters in a natural way. These rep...
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We argue that weak containment is an appropriate notion of amenability for inverse semigroups. Given an inverse semigroup S and a homomorphism φ of S onto a group G, we show, under an assumption on ker(φ), that S has weak containment if and only if G is amenable and ker(φ) has weak containment. Using Fell bundle amenability, we find a related result for inverse semigroups with zero. We show tha...
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In this paper, we apply the theory of inverse semigroups to the C∗-algebra U [Z] considered in [Cun08]. We show that the C∗-algebra U [Z] is generated by an inverse semigroup of partial isometries. We explicity identify the groupoid Gtight associated to the inverse semigroup and show that Gtight is exactly the same groupoid obtained in [CL10].
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We construct reduced and full semigroup C*-algebras for left cancellative semigroups. Our new construction covers particular cases already considered by A. Nica and also Toeplitz algebras attached to rings of integers in number fields due to J. Cuntz. Moreover, we show how (left) amenability of semigroups can be expressed in terms of these semigroup C*-algebras in analogy to the group case.
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ژورنال
عنوان ژورنال: Proceedings of the Edinburgh Mathematical Society
سال: 1985
ISSN: 0013-0915,1464-3839
DOI: 10.1017/s0013091500003187