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 (D1,D2)...

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Bibliographic Details
Published in:Journal of algebra 2020-02, Vol.544, p.302-328
Main Authors: Santulo, Ednei A., Souza, Jonathan P., Yasumura, Felipe Y.
Format: Article
Language:English
Subjects:
Associative algebras
Group gradings
Incidence algebras
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Summary: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 (D1,D2)-bimodules, where G is an abelian group, and D1 and D2 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.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2019.10.026