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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Bibliographic Details
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
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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
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Summary: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