$C^*$-extensions of non-self-adjoint dynamics

Abstract: Given the action of a group G on a non-self-adjoint operator algebra A, the crossed product of A by G can be realized as the subalgebra of a $C^*$-crossed product when the dynamics of G acting on A can be extended to self-adjoint dynamics of G acting on a $C^*$-algebra. In this talk, we characterize the existence of such a dynamical extension in terms of the boundary ideal structure for A in its maximal representation. We define a lattice structure for an operator algebra’s completely isometric representation theory and discuss how one might recover the crossed product of an operator algebra in a representation lacking a self-adjoint dynamical extension.

geometric topologynumber theoryoperator algebrasrepresentation theory

Audience: researchers in the topic

( paper | video )

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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 meet.google.com/zjd-ehrs-wtx (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.

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