Twisted partial actions and the Brauer group

• Grant number: 12/20425-3
• Support Opportunities: Research Grants - Visiting Researcher Grant - Brazil
• Start date: January 17, 2013
• End date: March 03, 2013
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Mikhailo Dokuchaev
• Grantee: Mikhailo Dokuchaev
• Visiting researcher: Antonio Paques
• Visiting researcher institution: Universidade Federal do Rio Grande do Sul (UFRGS). Instituto de Matemática (IM), Brazil
• 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 Antonio Paques we are going to continue our study of twisted partial actions of Hopf algebras and apply the theory of partial actions to the Brauer groups of commutative rings. In particular, as one of the goals, we shall investigate the globalization problem of twisted partial actions of Hopf algebras on algebras. As a second goal we shall study the relation between the relative Brauer group of a partial Galois extension of commutative rings and the group formed by the equivalence classes of all twistings of the partial action. (AU)