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SUMMARY:Rong Tang (Jilin University\, China)
DTSTART:20260406T150000Z
DTEND:20260406T160000Z
DTSTAMP:20260423T021313Z
UID:ENAAS/168
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ENAAS/168/">
 Homotopy theory of post-Lie algebras</a>\nby Rong Tang (Jilin University\,
  China) as part of European Non-Associative Algebra Seminar\n\n\nAbstract\
 nGuided by Koszul duality theory\, we consider the graded Lie algebra of c
 oderivations of the cofree conilpotent graded cocommutative cotrialgebra g
 enerated by $V$. We show that in the case of $V$ being a shift of an ungra
 ded vector space $W$\, Maurer-Cartan elements of this graded Lie algebra a
 re exactly  post-Lie algebra structures on $W$. The cohomology of a post-L
 ie algebra  is then defined using Maurer-Cartan twisting. The second cohom
 ology group of a post-Lie algebra has a familiar interpretation as equival
 ence classes of infinitesimal deformations. Next we define a post-Lie$_\\i
 nfty$ algebra structure  on a graded vector space to be a Maurer-Cartan el
 ement of the aforementioned graded Lie algebra. Post-Lie$_\\infty$ algebra
 s admit a useful characterization in terms of $L_\\infty$-actions (or open
 -closed homotopy Lie algebras). Finally\, we introduce the notion of homot
 opy Rota-Baxter operators on open-closed homotopy Lie algebras and show th
 at certain homotopy Rota-Baxter operators induce post-Lie$_\\infty$ algebr
 as. This is a joint work with Andrey Lazarev and Yunhe Sheng.\n
LOCATION:https://researchseminars.org/talk/ENAAS/168/
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