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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Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2023
ISSN:1815-0659
1. Verfasser: Catoire, Pierre
Format: Artikel
Sprache:Englisch
Veröffentlicht: Інститут математики НАН України 2023
Online Zugang: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
Zitieren: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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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