C* and geometric properties of inverse semigroups

Abstract: Inverse semigroups are a generalization of groups, where elements in an inverse semigroup can be thought of as partial symmetries of a space (instead of global symmetries, as in the group case). Out of these one can construct a uniform Roe algebra algebra just as in the group case, and study its properties. In this talk, we shall characterize when such C*-algebra is nuclear by means of an intrinsic metric in the semigroup, and prove that its nuclearity is equivalent to the semigroup having property A. Moreover, one can also study amenability notions in this case, and relate the trace space of the uniform Roe algebra with certain invariant measures in the semigroup. This talk is based on joint work with Pere Ara and Fernando Lledó.

geometric topologynumber theoryoperator algebrasrepresentation theory

Audience: researchers in the topic

( slides | video )

Noncommutative Geometry in NYC

Series comments: Noncommutative Geometry studies an interplay between spatial forms and algebras with non-commutative multiplication. Our seminar welcomes talks in Number Theory, Geometric Topology and Representation Theory linked to the context of Operator Algebras. All talks are kept at the entry-level accessible to the graduate students and non-experts in the field. To join us click sju.webex.com/meet/nikolaei (5 min in advance) and igor DOT v DOT nikolaev AT gmail DOT com to subscribe/unsubscribe for the mailing list, to propose a talk or to suggest a speaker. Pending speaker's consent, we record and publish all talks at the hyperlink "video" on speaker's profile at the "Past talks" section. The slides can be posted by providing the organizers with a link in the format "myschool.edu/~myfolder/myslides.pdf". The duration of talks is 1 hour plus or minus 10 minutes.