Partial actions, subshifts and related algebras

• Grant number: 15/21491-8
• Support Opportunities: Research Grants - Visiting Researcher Grant - Brazil
• Start date: January 04, 2016
• End date: March 03, 2016
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Mikhailo Dokuchaev
• Grantee: Mikhailo Dokuchaev
• Visiting researcher: Ruy Exel Filho
• Visiting researcher institution: Universidade Federal de Santa Catarina (UFSC). Centro de Ciências Físicas e Matemáticas, Brazil
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 15/09162-9 - Non commutative algebra and applications, AP.TEM

Abstract

During the visit of Professor Ruy Exel we plan to develop a research project in the area of partial actions and their applications to subshifts. In particular, we pretend to introduce an algebra (both abstract and $C^*$) associated to an arbitrary subshift X and a topological space, which we call the spectrum of X. The spectrum possesses a partial topological dynamics which is appropriate for an algebraic approach to X. We shall study the algebras and the spectrum related to X. We shall also treat algebras related to the Leavitt algebra L(m,n) by means of partial actions and partial representations. (AU)