Pseudo-Frobenius graded algebras with enough idempotents

TL;DR

This paper introduces pseudo-Frobenius graded algebras with enough idempotents, extending classical PF and QF ring concepts, and explores their properties and implications in representation theory.

Contribution

It defines pseudo-Frobenius graded algebras with enough idempotents and demonstrates their characterization via graded Nakayama forms and invariance under covering functors.

Findings

Characterization by graded Nakayama form

Preservation of pseudo-Frobenius property under covering functors

Relevance to representation theory

Abstract

We introduce and study the notion of pseudo-Frobenius graded algebra with enough idempotents, showing that it follows the pattern of the classical concept of pseudo-Frobenius (PF) and Quasi-Frobenius (QF) rings, in particular finite dimensional self-injective algebras, as studied by Nakayama, Morita, Faith, Tachikawa, etc. We show that such an algebra is characterized by the existence of a graded Nakayama form. Moreover, we prove that the pseudo-Frobenius property is preserved and reflected by covering functors, a fact that makes the concept useful in Representation Theory.