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SUMMARY:Yuri Bazlov (University of Manchester)
DTSTART:20240118T100000Z
DTEND:20240118T110000Z
DTSTAMP:20260423T035709Z
UID:EQuAL/19
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/EQuAL/19/">C
 ocycle and Galois cocycle twists of algebras\, representations and orders<
 /a>\nby Yuri Bazlov (University of Manchester) as part of European Quantum
  Algebra Lectures (EQuAL)\n\n\nAbstract\nIn a construction known as Drinfe
 ld twist\, a 2-cocycle on a Hopf algebra H is used to modify the coproduct
  on H as well as the associative product in any H-module algebra A. I am i
 nterested to know to what extent the representation theory of the twist of
  A can be recovered from that of A\; the A#H-module category\, unchanged u
 nder the twist\, plays a role here. I will talk about an application of th
 is idea to rational Cherednik-type algebras\, which led\, in a joint work 
 with E. Jones-Healey\, to establishing nontrivial isomorphisms between bra
 ided and classical versions of these algebras. Twists also help to approac
 h representation theory of the so-called mystic reflection groups\, define
 d by the Chevalley-Serre-Shephard-Todd property of their action on a quant
 um polynomial ring. An important source of twists\, motivated by torsors i
 n geometry\, should be cocycles arising from (Hopf-)Galois extensions of a
 lgebras\, and I will discuss this in the context of constructing orders an
 d normal integral bases in central simple algebras over a number field.\n
LOCATION:https://researchseminars.org/talk/EQuAL/19/
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