Quasi-triangular, triangular, factorizable anti-Leibniz bialgebras and anti-Leibniz Yang-Baxter equation
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909734532022272 |
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| author | Hou, Bo Cui, Zhanpeng |
| author_facet | Hou, Bo Cui, Zhanpeng |
| contents | We introduce the notion of an anti-Leibniz bialgebra which is equivalent to a Manin triple of anti-Leibniz algebras, is equivalent to a matched pair of anti-Leibniz algebras. The study of some special anti-Leibniz bialgebras leads to the introduction of the anti-Leibniz Yang-Baxter equation in an anti-Leibniz algebra. A symmetric (or an invariant) solution of the anti-Leibniz Yang-Baxter equation gives an anti-Leibniz bialgebra. The notion of a relative Rota-Baxter operator of an anti-Leibniz algebra is introduced to construct symmetric solutions of the anti-Leibniz Yang-Baxter equation. Moreover, we introduce the notions of factorizable anti-Leibniz bialgebras and skew-symmetric Rota-Baxter anti-Leibniz algebras, and show that a factorizable anti-Leibniz bialgebra leads to a factorization of the underlying anti-Leibniz algebra. There is a one-to-one correspondence between factorizable anti-Leibniz bialgebras and skew-quadratic Rota-Baxter anti-Leibniz algebras. Finally, we constrict anti-Leibniz bialgebras form Leibniz bialgebras by the tensor product and constrict infinite-dimensional anti-Leibniz bialgebras form finite-dimensional anti-Leibniz bialgebras by the completed tensor product. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_20028 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quasi-triangular, triangular, factorizable anti-Leibniz bialgebras and anti-Leibniz Yang-Baxter equation Hou, Bo Cui, Zhanpeng Rings and Algebras Quantum Algebra We introduce the notion of an anti-Leibniz bialgebra which is equivalent to a Manin triple of anti-Leibniz algebras, is equivalent to a matched pair of anti-Leibniz algebras. The study of some special anti-Leibniz bialgebras leads to the introduction of the anti-Leibniz Yang-Baxter equation in an anti-Leibniz algebra. A symmetric (or an invariant) solution of the anti-Leibniz Yang-Baxter equation gives an anti-Leibniz bialgebra. The notion of a relative Rota-Baxter operator of an anti-Leibniz algebra is introduced to construct symmetric solutions of the anti-Leibniz Yang-Baxter equation. Moreover, we introduce the notions of factorizable anti-Leibniz bialgebras and skew-symmetric Rota-Baxter anti-Leibniz algebras, and show that a factorizable anti-Leibniz bialgebra leads to a factorization of the underlying anti-Leibniz algebra. There is a one-to-one correspondence between factorizable anti-Leibniz bialgebras and skew-quadratic Rota-Baxter anti-Leibniz algebras. Finally, we constrict anti-Leibniz bialgebras form Leibniz bialgebras by the tensor product and constrict infinite-dimensional anti-Leibniz bialgebras form finite-dimensional anti-Leibniz bialgebras by the completed tensor product. |
| title | Quasi-triangular, triangular, factorizable anti-Leibniz bialgebras and anti-Leibniz Yang-Baxter equation |
| topic | Rings and Algebras Quantum Algebra |
| url | https://arxiv.org/abs/2412.20028 |