Partial actions and partial representations, cohomology and applications

• Grant number: 10/16578-3
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Duration: January 04, 2011 - January 02, 2012
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Mikhailo Dokuchaev
• Grantee: Mikhailo Dokuchaev
• Visiting researcher: Boris Novikov
• Visiting researcher institution: V.N. Karazin Kharkiv National University, Ukraine
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 09/52665-0 - Groups, rings and algebras: interactions and applications, AP.TEM

Abstract

We plan to continue our study of partial projective representations, partial Schur Multipliers, and to follow with the development the co-homological theory based on partial actions. We expect to elaborate the basic ingredients of such a theory, providing of the creation of its fundametals. As an important target in this direction, we shall initiate the development a theory of Brauer groups based on partial actions. We shall also continue our study of the immersion problem of the fibers into the generalized direct limits of vector spaces, aiming to obtain applications to algebraic Fell bundles. Moreover, we shall consider applications of partial actions of semigroups to the automata theory, in particular, we shall study a new concept based on partial actions, that of a pre-automaton. We shall treat globalizations of pre-automata and analyze the languages recognized by pre-automata and their globalizations, as well as the relations between deterministic pre-automata and the non-deterministic ones. (AU)