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SUMMARY:Loïc Foissy
DTSTART:20250509T130000Z
DTEND:20250509T140000Z
DTSTAMP:20260423T021526Z
UID:ACPMS/52
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ACPMS/52/">D
 ouble bialgebra of noncrossing partitions</a>\nby Loïc Foissy as part of 
 Algebraic and Combinatorial Perspectives in the Mathematical Sciences\n\n\
 nAbstract\nA double bialgebra is a family $(A\,m\,\\Delta\,\\delta)$ such 
 that both $(A\,m\,\\Delta)$ and $(A\,m\,\\delta)$ are bialgebras\, with th
 e extra condition that seeing $\\delta$ as a right coaction on itself\, $m
 $ and $\\Delta$ are right comodules morphism over $(A\,m\,\\delta)$. A cla
 ssical example is given by the polynomial algebra $\\mathbb{C}[X]$\, with 
 its two classical coproducts. In this talk\, we will present a double bial
 gebra structure on the symmetric algebra generated by noncrossing partitio
 ns. The first coproduct is given by the separations of the blocks of the p
 artitions\, with respect to the entanglement\, and the second one by fusio
 ns of blocks. This structure implies that there exists a unique polynomial
  invariant on noncrossing partitions which respects both coproducts: we wi
 ll give some elements on this invariant\, and applications to the antipode
  of noncrossing partitions.\n
LOCATION:https://researchseminars.org/talk/ACPMS/52/
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