Mathematics Seminar - 10/01/25

Abstract:

In noncommutative geometry it is often necessary to consider dense $*$-subalgebras of C$^*$-algebras, in particular, in connection with cyclic cohomology or with the study of unbounded derivations on C$^*$-algebras. Smooth subalgebras of noncommutative spaces are also naturally present in studying spectral triples.  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.   In analogy with the algebras of smooth functions on a compact manifold, such a smooth subalgebra should be closed under holomorphic functional calculus of all elements and under smooth-functional calculus of self-adjoint elements. It should also be complete with respect to a locally convex algebra topology.  The purpose of this talk is to define and study smooth subalgebras of Bunce-Deddens C$^*$-algebras as well as derivations on those smooth subalgebras.

Note:

Contact Prof. Shantia Yarahmadian at syarahmadian@math.msstate.edu or (662) 325-7143 for additional information.