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SUMMARY:Pierre Catoire (University of the Littoral Opal Coast\, France)
DTSTART:20240812T150000Z
DTEND:20240812T160000Z
DTSTAMP:20260423T021122Z
UID:ENAAS/82
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ENAAS/82/">T
 he free tridendriform algebra\, Schroeder trees and Hopf algebras</a>\nby 
 Pierre Catoire (University of the Littoral Opal Coast\, France) as part of
  European Non-Associative Algebra Seminar\n\n\nAbstract\nThe notions of de
 ndriform algebras\, respectively tridendriform\, describe the action of so
 me elements of the symmetric groups called shuffle\, respectively quasi-sh
 uffle over the set of words whose letters are elements of an alphabet\, re
 spectively of a monoid. A link between dendriform and tridendriform algebr
 as will be made. Those words algebras satisfy some properties but they are
  not free. This means that they satisfy extra properties like commutativit
 y. In this talk\, we will describe the free tridendriform algebra. It will
  be described with planar trees (not necessarily binary) called Schroeder 
 trees. We will describe the tridendriform structure over those trees in a 
 non-recursive way. Then\, we will build a coproduct on this algebra that w
 ill make it a (3\, 2)-dendriform bialgebra graded by the number of leaves.
  Once it will be build\, we will study this Hopf algebra: duality\, quotie
 nt spaces\, dimensions\, study of the primitives elements...\n
LOCATION:https://researchseminars.org/talk/ENAAS/82/
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