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SUMMARY:Yuri Bazlov (University of Manchester)
DTSTART:20250226T200000Z
DTEND:20250226T210000Z
DTSTAMP:20260420T053337Z
UID:NYC-NCG/187
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NYC-NCG/187/
 ">Cocycle twists of algebras\, representations and orders</a>\nby Yuri Baz
 lov (University of Manchester) as part of Noncommutative geometry in NYC\n
 \n\nAbstract\nA way to deform an associative algebra $A$ is to twist the\n
 multiplication by a 2-cocycle on a group or a Hopf algebra acting on\n$A$.
  I am interested to know to what extent the representations (and\nring-the
 oretic and homological properties) of the twist are determined\nby those o
 f $A$. My case in point will be rational Cherednik algebras\nover complex 
 reflection groups: twists of these well-studied objects\ngive algebras\, w
 ith similar PBW bases\, over "mystic reflection groups"\,\nand for some of
  them we can give an explicit combinatorial description\nof standard modul
 es(arXiv:2501.06673\, with Jones-Healey). Twists\ndescend to finite-dimens
 ional quotients of Cherednik algebras at $t=0$\,\nand over number fields\,
  seem to produce their forms (in the sense that\nthe twist trivializes ove
 r a field extension). This hints at an\ninterplay between twists and arith
 metic\; if time permits\, I will mention\na possible connection to Hopf-Ga
 lois structures on fields.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/187/
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