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SUMMARY:Homotopy theory of post-Lie algebras
DTSTART:20240620T081500Z
DTEND:20240620T094500Z
DTSTAMP:20240806T203300Z
UID:indico-event-828@events.gwdg.de
DESCRIPTION:Speakers: Rong Tang\n\nGuided by Koszul duality theory\, we co
nsider the graded Lie algebra of coderivations of the cofree conilpotent g
raded cocommutative cotrialgebra generated by $V$. We show that in the cas
e of $V$ being a shift of an ungraded vector space $W$\, Maurer-Cartan ele
ments of this graded Lie algebra are exactly post-Lie algebra structures
on $W$. The cohomology of a post-Lie algebra is then defined using Maur
er-Cartan twisting. The second cohomology group of a post-Lie algebra has
a familiar interpretation as equivalence classes of infinitesimal deformat
ions. Next we define a post-Lie$_\\infty$ algebra structure on a graded
vector space to be a Maurer-Cartan element of the aforementioned graded Li
e algebra. Post-Lie$_\\infty$ algebras admit a useful characterization in
terms of $L_\\infty$-actions (or open-closed homotopy Lie algebras). Final
ly\, we introduce the notion of homotopy Rota-Baxter operators on open-clo
sed homotopy Lie algebras and show that certain homotopy Rota-Baxter opera
tors induce post-Lie$_\\infty$ algebras. This is a joint work with Andrey
Lazarev and Yunhe Sheng.\n\nhttps://events.gwdg.de/event/828/
LOCATION:Sitzungszimmer (MI)
URL:https://events.gwdg.de/event/828/
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