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SUMMARY:Anastasia Doikou (Heriot-Watt University\, UK)
DTSTART:20240520T150000Z
DTEND:20240520T160000Z
DTSTAMP:20260423T052501Z
UID:ENAAS/70
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ENAAS/70/">P
 arametric set-theoretic Yang-Baxter equation: p-racks\, solutions & quantu
 m algebras</a>\nby Anastasia Doikou (Heriot-Watt University\, UK) as part 
 of European Non-Associative Algebra Seminar\n\n\nAbstract\nThe theory of t
 he parametric set-theoretic Yang-Baxter equation is established from a pur
 ely algebraic point of view.  We introduce generalizations of the familiar
  shelves and racks named parametric (p)-shelves and racks. These objects s
 atisfy a "parametric self-distributivity" condition and lead to solutions 
 of the Yang-Baxter equation. Novel\, non-reversible solutions are  obtaine
 d from p-shelve/rack solutions by a suitable parametric twist\, whereas al
 l reversible set-theoretic solutions are reduced to the identity map via a
  parametric twist. The universal algebras associated to both p-rack and ge
 neric parametric set-theoretic solutions are next presented and the corres
 ponding universal R-matrices are derived.  By introducing the concept of a
  parametric coproduct we prove the existence of a parametric co-associativ
 ity. We show that the parametric coproduct is an algebra homomorphsim and 
 the universal R-matrices intertwine with the algebra coproducts.\n
LOCATION:https://researchseminars.org/talk/ENAAS/70/
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