Partial actions, restriction semigroups and operator algebras

Abstract

During the visit of Professor Ganna Kudryavtseva we pretend to develop a research project in the area of partial actions, related topics and applications to operator algebras, abstract algebras and automata theory. In particular, we shall study the restriction semigroups and étale categories related to some classes of operator algebras. Moreover, we plan to elaborate and study appropriate notions of universal and tight categories for partial transformation categories, and versions of crossed products. We also will consider the problem of generalization of the theory of the Birget-Rhodes expansion for the context of partial monoid actions, on one hand, and for restriction semigrups, on the other. We also pretend to contribute to the theory of pre-automata, considering an appropriate concept of a syntactic congruence, to work out and investigate the corresponding notions of recognizable language varieties, and discuss other adjacent problems of automata theory. Since the beginning of the stay the Visitor will give a course on Automata Theory for master and PhD students of IME-USP, with two hours per week teaching load. (AU)