The group of automorphisms of the algebra of one-sided inverses of a polynomial algebra, II

TL;DR

This paper identifies explicit generators for the automorphism group of the algebra of one-sided inverses of a polynomial algebra and introduces an analogue of the polynomial Jacobian homomorphism.

Contribution

It provides the first explicit description of automorphisms for this algebra and establishes a new Jacobian-like homomorphism in this context.

Findings

Explicit generators for the automorphism group are constructed.

An analogue of the polynomial Jacobian homomorphism is introduced.

The structure of automorphisms in this algebra is characterized.

Abstract

Explicit generators are found for the group of automorphisms of the algebra of one-sided inverses of a polynomial algebra in $n$ variables. An analogue of the polynomial Jacobian homomorphism is found.