Holomorphic subalgebras of $n$-homogeneous $C^*$-algebras

Abstract: There is a long tradition of analyzing $C^*$-algebras through topological invariants. One such result is Tomiyama and Takesaki's 1961 proof that an $n$-homogeneous $C^*$-algebra is determined up to $*$-isomorphism by an underlying continuous matrix bundle. Suppose that the base space of the bundle is a bordered Riemann surface with finitely many smooth boundary components, and the interior of the bundle is holomorphic. Then for each such $n$-homogeneous $C^*$-algebra, one can define a holomorphic subalgebra. In this talk, we will describe some progress made towards classifying these subalgebras up to complete isometric isomorphism based on their underlying bundles, including some recent work with Jacob Cornejo.

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.