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SUMMARY:Oleg Aristov
DTSTART:20230207T150000Z
DTEND:20230207T160000Z
DTSTAMP:20260422T175440Z
UID:QGS/80
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/QGS/80/">Com
 plex-analytic approach to quantum groups</a>\nby Oleg Aristov as part of Q
 uantum Groups Seminar [QGS]\n\n\nAbstract\nWe discuss quantum analogues of
  complex Lie groups. Our approach is closer to classical quantum group the
 ory than to C*-algebraic one (no multipliers and no invariant weights). I 
 propose to consider a topological Hopf algebra with a finiteness condition
  (holomorphically finitely generated or HFG for short). This topic seems 
 to offer a wide range of research opportunities.\n\nOur focus is on exampl
 es\, such as analytic forms of some classical quantum groups (a deformatio
 n of a solvable Lie group and Drinfeld-Jimbo algebras). I also present som
 e general results: (1) the category of Stein groups is anti-equivalent to 
 the category of commutative Hopf HFG algebras\; (2) If G is a compactly ge
 nerated Lie group\, the associated convolution cocommutative topological H
 opf algebra (introduced by Akbarov) is HFG. When\, in addition\, G is conn
 ected and linear\, the structure of this cocommutative algebra can be desc
 ribed explicitly. I also plan to discuss briefly holomorphic duality (whic
 h is parallel to Pontryagin duality).\n
LOCATION:https://researchseminars.org/talk/QGS/80/
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