Partial representations and applications

• Grant number: 24/15812-5
• Support Opportunities: Research Grants - Visiting Researcher Grant - Brazil
• Start date: December 01, 2024
• End date: August 31, 2025
• 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: 20/16594-0 - Non commutative rings and applications, AP.TEM

Abstract

Based on the process of induction of ideals, introduced in 2017 by the present project participants in the context of partial crossed products, we plan to investigate the process of induction of partial representations of groups from representations of certain isotropy subgroups, as well as related issues. We shall also study the concept of the depth of a subshift X, defined in terms of the spectral space introduced in a previous work, where we gave a description of the corresponding Carlsen-Matsumoto C*-algebras as partial crossed products. We will introduce an algebraic analogue of the Carlsen-Matsumoto algebra over a field of characteristic zero and discuss its algebraic properties. (AU)