On Extended Associative Semigroups
We study extended associative semigroups (briefly, EAS), an algebraic structure used to define generalizations of the operad of associative algebras, and the subclass of commutative extended diassociative semigroups (briefly, CEDS), which are used to define generalizations of the operad of pre-Lie a...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2025 |
| Main Author: | |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2025
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/214192 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | On Extended Associative Semigroups. Loïc Foissy. SIGMA 21 (2025), 092, 34 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862600176272670720 |
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| author | Foissy, Loïc |
| author_facet | Foissy, Loïc |
| citation_txt | On Extended Associative Semigroups. Loïc Foissy. SIGMA 21 (2025), 092, 34 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We study extended associative semigroups (briefly, EAS), an algebraic structure used to define generalizations of the operad of associative algebras, and the subclass of commutative extended diassociative semigroups (briefly, CEDS), which are used to define generalizations of the operad of pre-Lie algebras. We give families of examples based on semigroups or on groups, as well as a classification of EAS of cardinality two. We then define linear extended associative semigroups as linear maps satisfying a variation of the braid equation. We explore links between linear EAS and bialgebras and Hopf algebras. We also study the structure of non-degenerate finite CEDS and show that they are obtained by semi-direct and direct products involving two groups.
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| first_indexed | 2026-03-21T12:22:01Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-214192 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-21T12:22:01Z |
| publishDate | 2025 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Foissy, Loïc 2026-02-20T07:59:51Z 2025 On Extended Associative Semigroups. Loïc Foissy. SIGMA 21 (2025), 092, 34 pages 1815-0659 2020 Mathematics Subject Classification: 20M75; 16S10; 18M60; 16T05 arXiv:2105.01326 https://nasplib.isofts.kiev.ua/handle/123456789/214192 https://doi.org/10.3842/SIGMA.2025.092 We study extended associative semigroups (briefly, EAS), an algebraic structure used to define generalizations of the operad of associative algebras, and the subclass of commutative extended diassociative semigroups (briefly, CEDS), which are used to define generalizations of the operad of pre-Lie algebras. We give families of examples based on semigroups or on groups, as well as a classification of EAS of cardinality two. We then define linear extended associative semigroups as linear maps satisfying a variation of the braid equation. We explore links between linear EAS and bialgebras and Hopf algebras. We also study the structure of non-degenerate finite CEDS and show that they are obtained by semi-direct and direct products involving two groups. The author thanks the anonymous referees for their useful and constructive comments on the first version of this text. The author acknowledges support from the grant ANR-20-CE40-0007 Combinatoire Algébrique, Résurgence, Probabilités Libres et Opérades. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications On Extended Associative Semigroups Article published earlier |
| spellingShingle | On Extended Associative Semigroups Foissy, Loïc |
| title | On Extended Associative Semigroups |
| title_full | On Extended Associative Semigroups |
| title_fullStr | On Extended Associative Semigroups |
| title_full_unstemmed | On Extended Associative Semigroups |
| title_short | On Extended Associative Semigroups |
| title_sort | on extended associative semigroups |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/214192 |
| work_keys_str_mv | AT foissyloic onextendedassociativesemigroups |