On tensor analogues of commuting automorphisms and central automorphisms

TL;DR

This paper introduces tensor analogues of commuting and central automorphisms, explores their properties, and applies these concepts to derive results concerning 2-Engel elements in algebraic structures.

Contribution

It presents the first tensor-based definitions of commuting and central automorphisms and investigates their properties and applications in algebra.

Findings

Properties of tensor automorphisms are established

Applications to 2-Engel elements are demonstrated

New algebraic insights are provided through tensor analogues

Abstract

In this paper, we introduce the tensor analogues of commuting automorphisms and central automorphisms. Then we give several properties of such automorphisms and apply these new concepts to give some interesting results for $2_\otimes$-Engel elements.