Ascolta

Description

Algebra is a branch of mathematics that deal algebraic structures such as groups, rings, fields, and algebras, and studies their properties and interactions. Algebra provides a unifying framework for many areas of mathematics, including number theory, geometry, topology, and mathematical physics, and has numerous applications in computer science, cryptography, and engineering.

Research Topics

The main focus of our research is the study of polynomial identities satisfied by an algebra over a field of characteristic zero, specifically the study of T-ideals of a free associative algebra using combinatorial and asymptotic methods related to the representation theory of the symmetric and general linear groups. The asymptotic calculation of the degrees of irreducible representations of the symmetric group in characteristic zero is well-known. An analysis of the cocharacter decomposition of an algebra into irreducible characters for the symmetric group allows us to obtain asymptotic evaluations that determine invariants of the corresponding varieties. To gain information about polynomial identities satisfied by an algebra, we attach to a T-ideal of polynomial identities some invariants such as the sequence of codimensions, the sequence of cocharacters, and the sequence of colengths. By studying their asymptotic behavior, we obtain classification results of the corresponding varieties.

Keywords

Algebras with polynomial identities; codimension; cocharacter; colengths; growth of varieties of associative and non-associative algebras.