Partial actions and partial representations

• Grant number: 13/19544-0
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Duration: March 02, 2014 - September 01, 2014
• 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

During the visit of Professor Boris Novikov we are going to continue our study of partial actions of groups, partial projective group representations, partial Schur multipliers of groups and the development of a cohomological theory based on partial actions. We expect to deepen our vision of the structure of the components of the partial Schur multiplier pM(G) of a group G and understand better the immersion of the usual Schur multiplier M(G) into pM(G). In order to obtain important material for elaboration of ideas and techniques we shall compute the partial Schur multipliers of some concrete groups. With respect to partial group cohomology we are going to improve our knowledge on the category pMod(G) of partial G-modules, in particular, to elaborate the concept of a "locally abelian category'' which is "covered'' by abelian categories in a way how pMod(G) does, and to develop a homological theory for such "locally abelian'' categories. We are planning also to calculate the partial cohomologies of some groups of small order and possibly of some particular classes of groups. We shall also investigate the globalization problem for partial group actions on sets with relations. (AU)