Superspecies and their representations

TL;DR

This paper introduces superspecies to construct all finite-dimensional superalgebras and classifies acyclic superspecies based on their graded representation types, advancing the understanding of superalgebra structures.

Contribution

It introduces graded equivalence, graded representation type, and graded species for finite group graded algebras, providing a framework for classification.

Findings

Classification of all acyclic superspecies

Introduction of graded equivalence and graded representation types

Framework for graded species in superalgebra theory

Abstract

Superspecies are introduced to provide the nice constructions of all finite-dimensional superalgebras. All acyclic superspecies, or equivalently all finite-dimensional (gr-basic) gr-hereditary superalgebras, are classified according to their graded representation types. To this end, graded equivalence, graded representation type and graded species are introduced for finite group graded algebras.