Mathematics – Operator Algebras
Scientific paper
1995-11-27
Mathematics
Operator Algebras
15 pages, plain TeX, no figures
Scientific paper
Given a group G, we construct, in a canonical way, an inverse semigroup S(G) associated to G. 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. In other words, G and S(G) have the same representation theory. We show that S(G) governs the subsemigroup of all closed linear subspaces of a G-graded C*-algebra, generated by the grading subspaces. In the special case of finite groups, the maximum number of such subspaces is computed. A ``partial'' version of the group C*-algebra of a discrete group is introduced. While the usual group C*-algebra of finite commutative groups forgets everything but the order of the group, we show that the partial group C*-algebra of the two commutative groups of order four, namely Z/4 and Z/2+Z/2, are not isomorphic.
No associations
LandOfFree
Partial actions of groups and actions of inverse semigroups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Partial actions of groups and actions of inverse semigroups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Partial actions of groups and actions of inverse semigroups will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-632630