SDU Operator Algebras Seminar

Title: Injective envelopes for partial C*-dynamical systems

Abstract: Given a C*-dynamical system, a fruitful avenue to study its properties has been to study the dynamics on its injective envelope. This approach relies on the result of Kalantar and Kennedy (2017), who show that C*-simplicity can be characterized via the Furstenberg boundary using injective envelope techniques. Inspired by this use case, we generalize the notion of injective envelope to partial C*-dynamical systems. Partial group actions are a generalization of group actions and first introduced for C*-algebras by Ruy Exel (1994) to express certain C*-algebras as crossed products by a single partial automorphism. In this talk, we give a short introduction to partial actions and show the existence of an injective envelope for unital partial C*-dynamical systems. Additionally, we discuss its connection to enveloping actions. This is based on joint work with Matthew Kennedy and Camila Sehnem.

Title: Algebras of one-sided subshifts over arbitrary alphabets

Abstract: Given an alphabet, which can be infinite, we consider subshifts defined by a set of forbidden words as a combinatorial object and define algebras associated with them. When the alphabet is finite, these include Carlsen's C*-algebras associated with subshifts. In this talk, I will explain how one naturally obtains a partial action from a subshift and how to use it to define the subshift algebras. As with graphs, even though we start with a combinatorial object, certain topological spaces arise from these algebras, one of them being the Ott-Tomforde-Willis (OTW) subshift. I will show how these C*-algebras are related to the conjugacy of Ott-Tomforde-Willis subshifts. At the end, I will briefly talk about the K-theory of the subshift C*-algebras. (Joint work with G. Boava, D. Gonçalves and D. van Wyk.)

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