BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Andrea Sciandra (University of Turin\, Italy) DTSTART:20250210T150000Z DTEND:20250210T160000Z DTSTAMP:20260423T052546Z UID:ENAAS/110 DESCRIPTION:Title: Yetter—Drinfeld post-Hopf algebras and Yetter—Drinfeld relative Rota —Baxter operators\nby Andrea Sciandra (University of Turin\, Italy) as part of European Non-Associative Algebra Seminar\n\n\nAbstract\nRecentl y\, Li\, Sheng and Tang introduced post-Hopf algebras and relative Rota— Baxter operators (on cocommutative Hopf algebras)\, providing an adjunctio n between the respective categories under the assumption that the structur es involved are cocommutative. We introduce Yetter— Drinfeld post-Hopf a lgebras\, which become usual post-Hopf algebras in the cocommutative setti ng. In analogy with the correspondence between cocommutative post-Hopf alg ebras and cocommutative Hopf braces\, the category of Yetter—Drinfeld po st-Hopf algebras is isomorphic to the category of Yetter—Drinfeld braces \, introduced by the author in a joint work with D. Ferri. The latter stru ctures are equivalent to matched pairs of actions on Hopf algebras and gen eralise both Hopf braces and Majid’s transmutation. We also prove that t he category of Yetter—Drinfeld post-Hopf algebras is equivalent to a sub category of Yetter—Drinfeld relative Rota—Baxter operators (that gener alise bijective relative Rota—Baxter operators on cocommutative Hopf alg ebras). Once the surjectivity of the latter operators is removed\, the equ ivalence is replaced by an adjunction and one recovers\, in the cocommutat ive case\, the result of Li\, Sheng and Tang. The talk is partially based on a joint work with D. Ferri.\n LOCATION:https://researchseminars.org/talk/ENAAS/110/ END:VEVENT END:VCALENDAR