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 M3//EN
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METHOD:PUBLISH
BEGIN:VEVENT
DTSTAMP:20251104T212210Z
DTSTART:20251112T120000Z
DTEND:20251112T130000Z
SUMMARY:Manchester Geometry Seminar - Andrey Lazarev
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}l15e-mhl2qf
 nt-ywe580
DESCRIPTION:Speaker: Andrey Lazarev (Lancaster)\n\nTitle: Duality for gra
 ded Lie algebras (joint work in progress with R. Tang)\n\nAbstract:\n\nG
 iven a finite-dimensional Lie algebra g\, its Chevalley-Eilenberg comple
 x CE(g) is an exterior algebra on g and its top exterior power could be 
 a nontrivial cocycle\, in which CE(g) has a kind of Poincare duality. Th
 is happens when g is unimodular i.e. when the trace of its adjoint repre
 sentation is zero. If this is not the case\, then there is still a twist
 ed version of duality for the cohomology of g\, similar to Poincare dual
 ity for nonorientable manifolds. These results belong to M. Hazewinkel a
 nd are over 50 years old.\n\nWhat happens when g is graded (or super) Li
 e algebra? In that case CE(g) is infinite-dimensional\, and on the face 
 of it\, there is no room for any analogues of the results mentioned abov
 e. Nevertheless\, there is a framework\, based on Koszul duality\, which
  extends duality to the graded context. Unsurprisingly\, the notion of t
 he Berezinian is relevant in this context.
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:Frank Adams Room 1\, Alan Turing Building\, Manchester
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