Finitely generated algebras with involution and their identities

TL;DR

This paper proves that any finitely generated associative algebra with involution over a zero characteristic field has a finite dimensional algebra with involution sharing the same identities, simplifying the study of such algebras.

Contribution

It establishes a finite dimensional reduction for finitely generated involutive associative algebras, advancing understanding of their identities.

Findings

Existence of finite dimensional algebra with same involutive identities

Reduction of infinite to finite dimensional cases

Simplification in the classification of involutive algebras

Abstract

Associative algebras with involution over a field of zero characteristic are considered. It is proved that in this case for any finitely generated associative algebra with involution there exists a finite dimensional algebra with involution which satisfies exactly the same identities with involution.