Smooth subalgebras in noncommutative geometry

Abstract: In noncommutative geometry it is often natural to consider dense *-subalgebras of C*-algebras in particular in connection with cyclic cohomology or with the study of unbounded derivations on C*-algebras. If C*-algebras are thought of as generalizations of topological spaces, then dense subalgebras may be regarded as specifying additional structures on the underlying space, like a smooth structure. At present there is no universally accepted general theory of such smooth subalgebras, however there is a number of "standard" examples defined and studied in the literature. In analogy with the algebras of smooth functions on a compact manifold, such a smooth subalgebra should have the following properties: (1) It should be closed under holomorphic functional calculus of all elements and under smooth-functional calculus of self-adjoint elements (2) It should be complete with respect to a locally convex algebra topology The purpose of the talk is to discuss those concepts on examples, including some more recent constructions.

geometric topologynumber theoryoperator algebrasrepresentation theory

Audience: researchers in the topic

( 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.