Representation rings of extensions of Hopf algebra of Kac-Paljutkin type
In this paper, we focus on studying two classes of finite dimensional $ \Delta $-associative algebras, which are extensions of a family of $ 2n^2 $-dimensional Kac-Paljutkin type semi-simple Hopf algebras $ H_{2n^2} $. All their indecomposable modules are classified. Furthermore, their representatio...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-09-01
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| Series: | Electronic Research Archive |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2024240 |
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| author | Dong Su Shilin Yang |
| author_facet | Dong Su Shilin Yang |
| author_sort | Dong Su |
| collection | DOAJ |
| description | In this paper, we focus on studying two classes of finite dimensional $ \Delta $-associative algebras, which are extensions of a family of $ 2n^2 $-dimensional Kac-Paljutkin type semi-simple Hopf algebras $ H_{2n^2} $. All their indecomposable modules are classified. Furthermore, their representation rings are described by generators with suitable relations. |
| format | Article |
| id | doaj-art-1a3704096c8f4b8296815e980ca93d98 |
| institution | Kabale University |
| issn | 2688-1594 |
| language | English |
| publishDate | 2024-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Electronic Research Archive |
| spelling | doaj-art-1a3704096c8f4b8296815e980ca93d982025-01-23T07:52:41ZengAIMS PressElectronic Research Archive2688-15942024-09-013295201523010.3934/era.2024240Representation rings of extensions of Hopf algebra of Kac-Paljutkin typeDong Su0Shilin Yang1School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, ChinaSchool of Mathematics, Statistics and Mechanics, Beijing University of Technology, Beijing 100124, ChinaIn this paper, we focus on studying two classes of finite dimensional $ \Delta $-associative algebras, which are extensions of a family of $ 2n^2 $-dimensional Kac-Paljutkin type semi-simple Hopf algebras $ H_{2n^2} $. All their indecomposable modules are classified. Furthermore, their representation rings are described by generators with suitable relations.https://www.aimspress.com/article/doi/10.3934/era.2024240$ \delta $-associative algebratensor productrepresentation ring |
| spellingShingle | Dong Su Shilin Yang Representation rings of extensions of Hopf algebra of Kac-Paljutkin type Electronic Research Archive $ \delta $-associative algebra tensor product representation ring |
| title | Representation rings of extensions of Hopf algebra of Kac-Paljutkin type |
| title_full | Representation rings of extensions of Hopf algebra of Kac-Paljutkin type |
| title_fullStr | Representation rings of extensions of Hopf algebra of Kac-Paljutkin type |
| title_full_unstemmed | Representation rings of extensions of Hopf algebra of Kac-Paljutkin type |
| title_short | Representation rings of extensions of Hopf algebra of Kac-Paljutkin type |
| title_sort | representation rings of extensions of hopf algebra of kac paljutkin type |
| topic | $ \delta $-associative algebra tensor product representation ring |
| url | https://www.aimspress.com/article/doi/10.3934/era.2024240 |
| work_keys_str_mv | AT dongsu representationringsofextensionsofhopfalgebraofkacpaljutkintype AT shilinyang representationringsofextensionsofhopfalgebraofkacpaljutkintype |