Separating invariants of finite groups

• Grant number: 21/01690-7
• Support Opportunities: Regular Research Grants
• Start date: July 01, 2021
• End date: June 30, 2023
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Artem Lopatin
• Grantee: Artem Lopatin
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

This project is dedicated to some problems in Invariant Theory. The notion of separating invariants was introduced by Derksen and Kemper in 2002 as simplification of the notion of generating set of an algebra. Namely, a subset S of the algebra of invariants F[W]^G is called separating if this set separates all elements of $W$ which can be separated by some invariants of F[W]^G. It is well-known that in many cases separating sets have better properties than invariants. By the results of Domokos, Draisma, Grosshans, Kemper, Wehlau it is known that for each algebra of invariants F[W]^G exists a minimal integer b_sep such that the set of all elements of F[W]^G with degrees less or equal to b_sep is separating. In this project, we will consider separating sets and b_sep for the algebra of multisymmetric polynomials and algebras of invariants of the group of pseudo-reflections and the alternating group. (AU)