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...
Збережено в:
| Опубліковано в: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2023 |
| ISSN: | 1815-0659 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2023
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/212018 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Tridendriform Structures. Pierre Catoire. SIGMA 19 (2023), 066, 36 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | 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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| ISSN: | 1815-0659 |