Group gradings on finite dimensional incidence algebras

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 \((...

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Published in:arXiv.org 2019-10
Main Authors: Santulo, Ednei A, Souza, Jonathan P, Yasumura, Felipe Y
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Language:English
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Algebra
Classification
Evaluation
Fields (mathematics)
Group theory
Incidence
Isomorphism
Subgroups
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description 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.
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subjects Algebra
Classification
Evaluation
Fields (mathematics)
Group theory
Incidence
Isomorphism
Subgroups
title Group gradings on finite dimensional incidence algebras
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