2-dimensional self-distributive non-counital bialgebras and knot invariants
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866912243890782208 |
|---|---|
| author | Bardakov, Valeriy G. Kozlovskaya, Tatiana A. Panasenko, Alexander S. Talalaev, Dmitry V. |
| author_facet | Bardakov, Valeriy G. Kozlovskaya, Tatiana A. Panasenko, Alexander S. Talalaev, Dmitry V. |
| contents | In the preprint of V. Bardakov, T. Kozlovskaya, D. Talalaev (Self-distributive bialgebras, arXiv:2501.19152) it was formulated a problem of classification of self-distributive bialgebras and was given classification of two-dimensional counital self-distributive bialgebras. In this paper, we consider non-counital case. We find all 2-dimensional algebras of this type. In constructed algebras we study the question of finding quandles for constructing knot invariants. This activity is part of the overall program for the linearization of the concepts of rack and quandle and the development of the representations theory of these structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_16875 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | 2-dimensional self-distributive non-counital bialgebras and knot invariants Bardakov, Valeriy G. Kozlovskaya, Tatiana A. Panasenko, Alexander S. Talalaev, Dmitry V. Quantum Algebra Group Theory In the preprint of V. Bardakov, T. Kozlovskaya, D. Talalaev (Self-distributive bialgebras, arXiv:2501.19152) it was formulated a problem of classification of self-distributive bialgebras and was given classification of two-dimensional counital self-distributive bialgebras. In this paper, we consider non-counital case. We find all 2-dimensional algebras of this type. In constructed algebras we study the question of finding quandles for constructing knot invariants. This activity is part of the overall program for the linearization of the concepts of rack and quandle and the development of the representations theory of these structures. |
| title | 2-dimensional self-distributive non-counital bialgebras and knot invariants |
| topic | Quantum Algebra Group Theory |
| url | https://arxiv.org/abs/2502.16875 |