Varieties of representations of groups and varieties of associative algebras

TL;DR

This paper explores the connections between varieties of group representations and associative algebra varieties, focusing on how group representation varieties are induced by algebra varieties, and discusses open problems in the field.

Contribution

It introduces the relationship between group representation varieties and associative algebra varieties, highlighting new links and open questions.

Findings

Identifies relations between group representation varieties and associative algebra varieties

Provides a list of open problems in the area

Highlights the induction of group representation varieties by algebra varieties

Abstract

The goal of this paper is to consider some relations between varieties of representations of groups and varieties of associative algebras. The main emphasis is put on the varieties of representations of groups induced by the varieties of associative algebras. We provide the reader with the list of some open problems.