Analysis Seminar

Thursday, February 9, 2023 4:00 pm - 4:00 pm EST (GMT -05:00)

Camila Sehnem, Department of Pure Mathematics, University of Waterloo

"C*-envelopes and semigroup C*-algebras"

The C*-envelope of an operator algebra C is the smallest C*-algebra generated by a completely isometric copy of C. In this talk I will consider the C*-envelope of the non-selfadjoint operator algebra generated by the canonical isometric representation of a semigroup P on $\ell^2(P)$, where $P$ is assumed to be a submonoid of a group.  I will show that the C*-envelope of this algebra is canonically isomorphic to the boundary quotient of the Toeplitz algebra of P. If time permits, I will discuss a similar result in a more general setting, in which the semigroup of isometries is replaced by a product system of C*-correspondences.

This seminar will be held both online and in person: