Tridendriform Structures

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2023
• Main Author: Catoire, Pierre
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2023
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/212018
• 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

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...