Identities for mixed representations of quiver are finitely based

TL;DR

This paper establishes a finite generating set for the identities of polynomial invariants in mixed quiver representations, extending classical representation theory to include bilinear forms.

Contribution

It introduces a finite basis for the T-ideal of identities in mixed quiver representations, advancing the understanding of their algebraic invariants.

Findings

Finite generating set for T-ideal of identities constructed

Extends classical quiver representation theory to mixed cases

Provides algebraic tools for analyzing polynomial invariants

Abstract

The classical construction of representations of quivers enables us to consider linear maps between several vector spaces. The mixed representations of quivers helps us to work with linear maps as well as bilinear forms on several vector spaces. We construct a finite generating set for the T-ideal of identities of the polynomial invariants of mixed representations of a quiver.