BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Shuai Hou (Jilin University\, China) DTSTART:20260831T150000Z DTEND:20260831T160000Z DTSTAMP:20260825T025048Z UID:ENAAS/206 DESCRIPTION:Title: Averaging Lie bialgebras\nby Shuai Hou (Jilin University\, China) as p art of European Non-Associative Algebra Seminar\n\nInteractive livestream: https://us02web.zoom.us/j/7803181064\n\nAbstract\nIn this talk\, we estab lish a bialgebra theory for averaging Lie algebras. First we introduce the notion of a quadratic averaging Lie algebra and show that it induces an i somorphism from the adjoint representation to the coadjoint representation . Then we introduce the notion of matched pairs\, Manin triples and bialge bras for averaging Lie algebras\, and show that Manin triples\, bialgebras and certain matched pairs of averaging Lie algebras are equivalent. In pa rticular\, we introduce the notion of an averaging operator on a quadratic Rota-Baxter Lie algebra which can induce an averaging Lie bialgebra natur ally.Finally\, we introduce the notion of the classical Yang-Baxter equati on in an averaging Lie algebra whose solutions give rise to averaging Lie bialgebras. We also introduce the notion of relative Rota-Baxter operators on an averaging Lie algebra and averaging pre-Lie algebras\, and construc t solutions of the classical Yang-Baxter equation in terms of relative Rot a-Baxter operators and averaging pre-Lie algebras. This work joint with Yu nhe Sheng and Yanqiu Zhou.\n LOCATION:https://researchseminars.org/talk/ENAAS/206/ URL:https://us02web.zoom.us/j/7803181064 END:VEVENT END:VCALENDAR