Adam Humeniuk, Department of Pure Mathematics, University of Waterloo
"On C*-Envelopes of Semicrossed Products"
A crossed product is a C*-algebra that encodes the action of a group on another C*-algebra, or on a topological space. Built analogously, a semicrossed product is a non-selfadjoint operator algebra that encodes the action of a semigroup on a C*-or-operator algebra. Any operator algebra has a unique minimal C*-algebra it generates, called its C*-envelope. The natural question is: When does the C*-envelope of a semicrossed product have the structure of a crossed product?
I will review crossed products and C*-envelopes, and explain the basics of semicrossed products. After reviewing some known positive results in this direction, I will explain how to show that the C*-envelope of a ``Nica-covariant" semicrossed product is a full corner in a crossed product, in the setting of any ``lattice ordered" abelian semigroup. This extends a result of Davidson, Fuller, and Kakariadis for the semigroup $\mathbb{Z}_+^n$ to a much wider class of semigroups, via a new approach.
MC 5417