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:20260914T071059Z UID:ENAAS/206 DESCRIPTION:Title: Averaging Lie bialgebras\nby Shuai Hou (Jilin University\, China) as p art of European Non-Associative Algebra Seminar\n\n\nAbstract\nIn this tal k\, we establish a bialgebra theory for averaging Lie algebras. First we i ntroduce the notion of a quadratic averaging Lie algebra and show that it induces an isomorphism from the adjoint representation to the coadjoint re presentation. Then we introduce the notion of matched pairs\, Manin triple s and bialgebras for averaging Lie algebras\, and show that Manin triples\ , bialgebras and certain matched pairs of averaging Lie algebras are equiv alent. In particular\, we introduce the notion of an averaging operator on a quadratic Rota-Baxter Lie algebra which can induce an averaging Lie bia lgebra naturally.Finally\, we introduce the notion of the classical Yang-B axter equation in an averaging Lie algebra whose solutions give rise to av eraging Lie bialgebras. We also introduce the notion of relative Rota-Baxt er operators on an averaging Lie algebra and averaging pre-Lie algebras\, and construct solutions of the classical Yang-Baxter equation in terms of relative Rota-Baxter operators and averaging pre-Lie algebras. This work j oint with Yunhe Sheng and Yanqiu Zhou.\n LOCATION:https://researchseminars.org/talk/ENAAS/206/ END:VEVENT END:VCALENDAR