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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.19690 |
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| _version_ | 1866911125096890368 |
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| author | Aliev, Ramil K. |
| author_facet | Aliev, Ramil K. |
| contents | Ruth J.Lawrence introduced a notion of a 3-algebra to construct invariants of 3-manifolds based on their triangulations in her paper "Algebras and triangular relations". Her primary definition is suitable for certain triangulations only although a hint to handle arbitrary ones has been proposed. Here I introduce an analogue of Frobenius compatibility for one class of 3-algebras hence I obtain a way to construct a full 3-algebra. Additionally, I provide with examples of a 3-algebra and invariants for lens spaces. Moreover, it leads to a new family of pentagon equations solutions: arising from projectors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_19690 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On an analogue of Frobenius formalism for 3-algebras and pentagon equations solutions arising from projectors Aliev, Ramil K. Quantum Algebra Ruth J.Lawrence introduced a notion of a 3-algebra to construct invariants of 3-manifolds based on their triangulations in her paper "Algebras and triangular relations". Her primary definition is suitable for certain triangulations only although a hint to handle arbitrary ones has been proposed. Here I introduce an analogue of Frobenius compatibility for one class of 3-algebras hence I obtain a way to construct a full 3-algebra. Additionally, I provide with examples of a 3-algebra and invariants for lens spaces. Moreover, it leads to a new family of pentagon equations solutions: arising from projectors. |
| title | On an analogue of Frobenius formalism for 3-algebras and pentagon equations solutions arising from projectors |
| topic | Quantum Algebra |
| url | https://arxiv.org/abs/2508.19690 |