On commutative set-theoretic solutions of the Pentagon Equation
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917646778236928 |
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| author | Castelli, Marco |
| author_facet | Castelli, Marco |
| contents | We extend the so-called retract relation given in [6] for involutive set-theoretic solutions of the Pentagon Equation and we introduce the notion of associated permutation group to study the family of the commutative non-degenerate ones. Moreover, we develop a machinery to construct all these solutions and we use it to give a quite explicit classification of the irretractable ones. Finally, non-degenerate solutions on left-zero semigroup are studied in detail, with an emphasis on the ones with cyclic associated permutation group and on the ones having small size. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_13758 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On commutative set-theoretic solutions of the Pentagon Equation Castelli, Marco Quantum Algebra 81R50 20M99 We extend the so-called retract relation given in [6] for involutive set-theoretic solutions of the Pentagon Equation and we introduce the notion of associated permutation group to study the family of the commutative non-degenerate ones. Moreover, we develop a machinery to construct all these solutions and we use it to give a quite explicit classification of the irretractable ones. Finally, non-degenerate solutions on left-zero semigroup are studied in detail, with an emphasis on the ones with cyclic associated permutation group and on the ones having small size. |
| title | On commutative set-theoretic solutions of the Pentagon Equation |
| topic | Quantum Algebra 81R50 20M99 |
| url | https://arxiv.org/abs/2404.13758 |