Skew-symmetric identities of finitely generated alternative algebras

TL;DR

This paper establishes a universal property of multilinear skew-symmetric polynomials in n-generated alternative algebras, showing they vanish under certain conditions, extending previous specific cases.

Contribution

It proves a general vanishing result for multilinear skew-symmetric polynomials in n-generated alternative algebras over characteristic zero fields, generalizing earlier specific cases.

Findings

Existence of a bound N(n) for vanishing polynomials

Extension of previous results to all multilinear skew-symmetric polynomials

Applicable to all n-generated alternative algebras over characteristic zero fields

Abstract

We prove that for every natural number n there exists a natural number N(n) such that every multilinear skew-symmetric polynomial on N(n) or more variables which vanishes in the free associative algebra vanishes as well in any n-generated alternative algebra over a field of characteristic 0. Before this was proved only for a series of such polynomials constructed by the author in [7].