Strongly Stable Automorphisms of the Categories of the Finitely Generated Free Algebras of the some Varieties of Linear Algebras

TL;DR

This paper investigates the automorphisms of categories of finitely generated free algebras in certain linear algebra varieties over characteristic 0 fields, focusing on their structure and implications for algebraic equivalences.

Contribution

It computes the quotient groups of automorphism groups over inner automorphisms for these categories, clarifying the distinction between geometric and automorphic equivalences.

Findings

Calculated quotient groups for various algebra varieties

Identified differences between geometric and automorphic equivalences

Provided structural insights into automorphism groups

Abstract

In this paper we consider some classical varieties of linear algebras over the field which has characteristic 0. For every considered variety we take a category of the finite generated free algebras of this variety. And for every this category we calculate the quotient group of the group of the all automorphisms of this category over the subgroup of the all inner automorphisms. This quotient group measures difference between the geometric equivalence and automorphic equivalence of algebras from this variety.