Noncommutative Novikov bialgebras and differential antisymmetric infinitesimal bialgebras with weight
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866910885810798592 |
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| author | Zheng, Shanghua Li, Yizhen Yang, Liushuting Guo, Li |
| author_facet | Zheng, Shanghua Li, Yizhen Yang, Liushuting Guo, Li |
| contents | This paper first develops a bialgebra theory for a noncommutative Novikov algebra, called a noncommutative Novikov bialgebra, which is further characterized by matched pairs and Manin triples of noncommutative Novikov algebras. The classical Yang-Baxter type equation, $\mathcal{O}$-operators, and noncommutative pre-Novikov algebras are introduced to study noncommutative Novikov bialgebra. As an application, noncommutative pre-Novikov algebras are obtained from differential dendriform algebras. Next, to generalize Gelfand's classical construction of a Novikov algebra from a commutative differential algebra to the bialgebra context in the noncommutative case, we establish antisymmetric infinitesimal (ASI) bialgebras for (noncommutative) differential algebras, and obtain the condition under which a differential ASI bialgebra induces a noncommutative Novikov bialgebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_15701 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Noncommutative Novikov bialgebras and differential antisymmetric infinitesimal bialgebras with weight Zheng, Shanghua Li, Yizhen Yang, Liushuting Guo, Li Rings and Algebras Representation Theory 16T10, 12H05, 17B38, 17D25, 16T25, 17A36, 17A30 This paper first develops a bialgebra theory for a noncommutative Novikov algebra, called a noncommutative Novikov bialgebra, which is further characterized by matched pairs and Manin triples of noncommutative Novikov algebras. The classical Yang-Baxter type equation, $\mathcal{O}$-operators, and noncommutative pre-Novikov algebras are introduced to study noncommutative Novikov bialgebra. As an application, noncommutative pre-Novikov algebras are obtained from differential dendriform algebras. Next, to generalize Gelfand's classical construction of a Novikov algebra from a commutative differential algebra to the bialgebra context in the noncommutative case, we establish antisymmetric infinitesimal (ASI) bialgebras for (noncommutative) differential algebras, and obtain the condition under which a differential ASI bialgebra induces a noncommutative Novikov bialgebra. |
| title | Noncommutative Novikov bialgebras and differential antisymmetric infinitesimal bialgebras with weight |
| topic | Rings and Algebras Representation Theory 16T10, 12H05, 17B38, 17D25, 16T25, 17A36, 17A30 |
| url | https://arxiv.org/abs/2503.15701 |