Partial actions, restriction semigroups and operator algebras

• Grant number: 14/23853-1
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: April 01, 2015
• End date: June 29, 2015
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Mikhailo Dokuchaev
• Grantee: Mikhailo Dokuchaev
• Visiting researcher: Ganna Kudryavtseva
• Visiting researcher institution: Institute Jožef Stefan (IJS), Slovenia
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

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)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

DOKUCHAEV, MIKHAILO; KIRICHENKO, VLADIMIR; KUDRYAVTSEVA, GANNA; PLAKHOTNYK, MAKAR. The max-plus algebra of exponent matrices of tiled orders. Journal of Algebra, v. 490, p. 1-20, NOV 15 2017. (15/09162-9, 13/11350-2, 15/16726-6, 14/23853-1)