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SUMMARY:Dietrich Burde (University of Vienna\, Austria)
DTSTART:20230227T150000Z
DTEND:20230227T160000Z
DTSTAMP:20260423T021130Z
UID:ENAAS/8
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ENAAS/8/">Pr
 e-Lie algebra structures on reductive Lie algebras and etale affine repres
 entations</a>\nby Dietrich Burde (University of Vienna\, Austria) as part 
 of European Non-Associative Algebra Seminar\n\n\nAbstract\nEtale affine re
 presentations of Lie algebras and algebraic groups arise in the context\no
 f affine geometry on Lie groups\, operad theory\, deformation theory and Y
 oung-Baxter equations.\nFor reductive groups\, every etale affine represen
 tation is equivalent to a\nlinear representation and we obtain a special c
 ase of a prehomogeneous representation.\nSuch representations have been cl
 assified by Sato and Kimura in some cases. The induced\nrepresentation on 
 the Lie algebra level gives rise to a pre-Lie algebra structure on the\nLi
 e algebra g of G. For a Lie group G\, a pre-Lie algebra structure on g cor
 responds to a\nleft-invariant affine structure on G. This refers to a well
 -known question by John Milnor from 1977\non the existence of complete lef
 t-invariant affine structures on solvable Lie groups.\n\nWe present result
 s on the existence of etale affine representations of reductive groups and
  Lie algebras\nand discuss a related conjecture of V. Popov concerning fla
 ttenable groups and linearizable\nsubgroups of the affine Cremona group.\n
LOCATION:https://researchseminars.org/talk/ENAAS/8/
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