# Group gradings on finite dimensional incidence algebras

## TL;DR

This paper classifies group gradings on finite-dimensional incidence algebras over fields with certain characteristics and explores the structure of related bimodules, leading to a comprehensive understanding of their isomorphism classes.

## Contribution

It provides a complete classification of group gradings on incidence algebras and analyzes the structure of associated bimodules, extending existing knowledge.

## Key findings

- Classification of group gradings over specified fields
- Structural description of $G$-graded bimodules
- Complete isomorphism classification of gradings

## Abstract

In this work, we classify the group gradings on finite-dimensional incidence algebras over a field, where the field has characteristic zero, or the characteristic is greater than the dimension of the algebra, or the grading group is abelian. Moreover, we investigate the structure of $G$-graded $(D_1,D_2)$-bimodules, where $G$ is an abelian group, and $D_1$ and $D_2$ are the group algebra of finite subgroups of $G$. As a consequence, we can provide a more profound structure result concerning the group gradings on the incidence algebras, and we can classify their isomorphism classes of group gradings.