Group gradings on finite dimensional incidence algebras
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2019
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| _version_ | 1866913222460702720 |
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| author | Santulo Jr., Ednei A. Souza, Jonathan P. Yasumura, Felipe Y. |
| author_facet | Santulo Jr., Ednei A. Souza, Jonathan P. Yasumura, Felipe Y. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1905_08391 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Group gradings on finite dimensional incidence algebras Santulo Jr., Ednei A. Souza, Jonathan P. Yasumura, Felipe Y. Rings and Algebras 16W50 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. |
| title | Group gradings on finite dimensional incidence algebras |
| topic | Rings and Algebras 16W50 |
| url | https://arxiv.org/abs/1905.08391 |