Averaging operators on groups and Hopf algebras
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915257555877888 |
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| author | Zhang, Huhu Gao, Xing |
| author_facet | Zhang, Huhu Gao, Xing |
| contents | Rota-Baxter operators on groups were studied quite recently. Motivated mainly by the fact that weight zero Rota-Baxter operators and averaging operators are Koszul dual to each other, we propose the concepts of averaging group and averaging Hopf algebra, and study relationships among them and the existing averaging Lie algebras. We also show that an averaging group induces a disemigroup and a rack, respectively. As the free object is one of the most significant objects in a category, we also construct explicitly the free averaging group on a set. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_11600 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Averaging operators on groups and Hopf algebras Zhang, Huhu Gao, Xing Rings and Algebras Group Theory 22E60, 08B20, 17B40 16W99 Rota-Baxter operators on groups were studied quite recently. Motivated mainly by the fact that weight zero Rota-Baxter operators and averaging operators are Koszul dual to each other, we propose the concepts of averaging group and averaging Hopf algebra, and study relationships among them and the existing averaging Lie algebras. We also show that an averaging group induces a disemigroup and a rack, respectively. As the free object is one of the most significant objects in a category, we also construct explicitly the free averaging group on a set. |
| title | Averaging operators on groups and Hopf algebras |
| topic | Rings and Algebras Group Theory 22E60, 08B20, 17B40 16W99 |
| url | https://arxiv.org/abs/2412.11600 |