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SUMMARY:Oleg Yu. Aristov (Moscow State University)
DTSTART:20220406T140000Z
DTEND:20220406T150000Z
DTSTAMP:20260420T052529Z
UID:NYC-NCG/93
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NYC-NCG/93/"
 >Complex analytic quantum groups</a>\nby Oleg Yu. Aristov (Moscow State Un
 iversity) as part of Noncommutative geometry in NYC\n\n\nAbstract\nWe disc
 uss a missing link in quantum group theory - quantum analogues of complex 
 Lie groups. As such analogues\, I propose to take topological Hopf algebra
 s with a finiteness condition (holomorphically finitely generated or HFG 
 for short). This approach is not directly related to C*-algebraic quantum 
 groups (at least for now) but is an alternative view.  Nevertheless\, the 
 topic seems to offer a wide range of research opportunities.\n\nOur focus 
 is on examples\, such as analytic forms of some classical quantum groups (
 a deformation of a solvable Lie group and  Drinfeld-Jimbo algebras).  I al
 so present some general results: 1) the category of Stein groups is anti-e
 quivalent  to the category of commutative Hopf HFG algebras\; 2) If $G$ is
  a compactly generated Lie group\, the  cocommutative topological Hopf alg
 ebra $\\widehat{A(G)}$ (naturally associated with $G$)  is  HFG.  When in 
 addition\, $G$ is connected linear\,  the structure of $\\widehat{A(G)}$ c
 an be described explicitly.\n\nI also plan to discuss briefly holomorphic 
 duality in the sense of Akbarov (which is parallel to Pontryagin duality).
 \n
LOCATION:https://researchseminars.org/talk/NYC-NCG/93/
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