BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Loïc Foissy (University of the Littoral Opal Coast\, France) DTSTART:20250303T150000Z DTEND:20250303T160000Z DTSTAMP:20260423T035529Z UID:ENAAS/113 DESCRIPTION:Title: Double bialgebra of noncrossing partitions\nby Loïc Foissy (Universit y of the Littoral Opal Coast\, France) as part of European Non-Associative Algebra Seminar\n\n\nAbstract\nA double bialgebra is a family $(A\,m\,\\D elta\,\\delta)$ such that both $(A\,m\,\\Delta)$ and $(A\,m\,\\delta)$ are bialgebras\, with the extra condition that seeing $\\delta$ as a right co action on itself\, $m$ and $\\Delta$ are right comodules morphism over $(A \,m\,\\delta)$. A classical example is given by the polynomial algebra $\\ mathbb{C}[X]$\, with its two classical coproducts. In this talk\, we will present a double bialgebra structure on the symmetric algebra generated by noncrossing partitions. The first coproduct is given by the separations o f the blocks of the partitions\, with respect to the entanglement\, and th e second one by fusions of blocks. This structure implies that there exist s a unique polynomial invariant on noncrossing partitions which respects b oth coproducts: we will give some elements on this invariant\, and applica tions to the antipode of noncrossing partitions.\n LOCATION:https://researchseminars.org/talk/ENAAS/113/ END:VEVENT END:VCALENDAR