Ruy Exel

TL;DR: In this article, the authors studied C *-algebras possessing an action of the circle group, from the point of view of their internal structure and their K-theory.

TL;DR: In this paper, the authors describe a special class of representations of an inverse semigroup S on Hilbert's space which they term tight, which are supported on a subset of the spectrum of the idempotent semilattice of S, 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.

TL;DR: In this paper, an inverse semigroup S(G) associated to a group G is constructed, in a canonical way, and the actions of S (G) are shown to be in one-to-one correspondence with the partial actions of G, both in the case of actions on a set, and that of actions as operators on a Hilbert space.

TL;DR: In this paper, the cross product A × α G is shown to be associative, provided that A is semiprime and that G is a cross product of a partial action of a group on an associative algebra.

TL;DR: In this paper, the authors studied the associativity of partial actions of groups on algebras and partial representations, and showed that a partial action of a group on an associative algebra G is associative, provided that all ideals of A are idempotent.