Seminar "Functional analysis and noncommutative geometry". Speaker: Dmitry Golubenko

Our original goal is to understand whether or not the C*-envelope of the free product  A_1*A_2*...of operator algebras is isomorphic to the free product of their C*-envelopes. It turns out that a similar result holds for Nica tensor algebras associated to semigroups. Following  https://arxiv.org/pdf/1804.10546.pdf and https://arxiv.org/pdf/1801.07296.pdf, I will define Nica tensor algebras, Senhem C*-algebras, and will show that the C*-envelopes of Nica tensor algebras are isomorphic to Senhem algebras. All the necessary concepts will be introduced along the way.