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...
Gespeichert in:
| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Datum: | 2023 |
| ISSN: | 1815-0659 |
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2023
|
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/212018 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Tridendriform Structures. Pierre Catoire. SIGMA 19 (2023), 066, 36 pages |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | 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.
|
|---|---|
| ISSN: | 1815-0659 |