Tridendriform Structures
Inspired by the work of J-L. Loday and M. Ronco, we build free tridendriform algebras over reduced trees, and we show that they have a coproduct satisfying some compatibilities with the tridendriform products. Its graded dual is the opposite bialgebra of TSym introduced by N. Bergeron et al., which...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2023 |
| Main Author: | |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2023
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/212018 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Tridendriform Structures. Pierre Catoire. SIGMA 19 (2023), 066, 36 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862719686995607552 |
|---|---|
| author | Catoire, Pierre |
| author_facet | Catoire, Pierre |
| citation_txt | Tridendriform Structures. Pierre Catoire. SIGMA 19 (2023), 066, 36 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Inspired by the work of J-L. Loday and M. Ronco, we build free tridendriform algebras over reduced trees, and we show that they have a coproduct satisfying some compatibilities with the tridendriform products. Its graded dual is the opposite bialgebra of TSym introduced by N. Bergeron et al., which is described by the lightning splitting of a tree. In particular, we can split the product into three pieces and the coproduct into two pieces with Hopf compatibilities. We generate its codendriform primitives and count its coassociative primitives thanks to L. Foissy's work.
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| first_indexed | 2026-03-21T00:40:22Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212018 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-21T00:40:22Z |
| publishDate | 2023 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Catoire, Pierre 2026-01-22T09:19:37Z 2023 Tridendriform Structures. Pierre Catoire. SIGMA 19 (2023), 066, 36 pages 1815-0659 2020 Mathematics Subject Classification: 16S10; 16T05; 16T10; 16W50; 17A30 arXiv:2207.03839 https://nasplib.isofts.kiev.ua/handle/123456789/212018 https://doi.org/10.3842/SIGMA.2023.066 Inspired by the work of J-L. Loday and M. Ronco, we build free tridendriform algebras over reduced trees, and we show that they have a coproduct satisfying some compatibilities with the tridendriform products. Its graded dual is the opposite bialgebra of TSym introduced by N. Bergeron et al., which is described by the lightning splitting of a tree. In particular, we can split the product into three pieces and the coproduct into two pieces with Hopf compatibilities. We generate its codendriform primitives and count its coassociative primitives thanks to L. Foissy's work. I want to thank all members of the LMPA at Université du Littoral Côte d’Opale for welcoming me to prepare my PhD. I especially thank Loıc Foissy, my PhD advisor. I thank the other PhD students of the LMPA for useful discussions, which gave me some ideas. I also want to thank the referees for the careful reading of this paper. 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 Tridendriform Structures Article published earlier |
| spellingShingle | Tridendriform Structures Catoire, Pierre |
| title | Tridendriform Structures |
| title_full | Tridendriform Structures |
| title_fullStr | Tridendriform Structures |
| title_full_unstemmed | Tridendriform Structures |
| title_short | Tridendriform Structures |
| title_sort | tridendriform structures |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212018 |
| work_keys_str_mv | AT catoirepierre tridendriformstructures |