The Jacobian Conjecture, together with Specht and Burnside-type problems

TL;DR

This paper investigates a novel algebraic approach to the Jacobian Conjecture, highlighting connections with algebra identities, mathematical physics, and automorphisms of polynomial algebras, based on Yagzhev's work.

Contribution

It introduces a new perspective on the Jacobian Conjecture using algebra identities linked to Yagzhev's approach, bridging multiple mathematical disciplines.

Findings

Identifies connections between algebra identities and the Jacobian Conjecture

Proposes a framework linking algebraic identities to automorphisms of polynomial algebras

Suggests potential pathways for resolving the Jacobian Conjecture

Abstract

We explore an (unpublished) approach to the famous Jacobian Conjecture by means of identities of algebras, discovered by the brilliant deceased mathematician, Alexander Vladimirovich Yagzhev (1951{2001). This approach also indicates some very close connections between mathematical physics, universal algebra and automorphisms of polynomial algebras