SMS scnews item created by Kevin Coulembier at Wed 7 Mar 2018 1154
Type: Seminar
Distribution: World
Expiry: 2 May 2018
Calendar1: 16 Mar 2018 1200-1300
CalLoc1: Carslaw 375
CalTitle1: Algebra Seminar: Vinberg’s problem for classical Lie algebras
Auth: kevinc@pkevinc.pc (assumed)

# Algebra Seminar: Molev -- Vinberg’s problem for classical Lie algebras

Alexander Molev (University of Sydney)

Friday 16 March, 12-1pm, Place: Carslaw 375

Title: Vinberg’s problem for classical Lie algebras

Abstract: The symmetric algebra S(g) of a Lie algebra g is equipped with the Poisson-Lie
bracket.  A family of Poisson commutative subalgebras can be produced by "shifting the
arguments" of g-invariants of S(g).  Vinberg’s problem stated in 1990 concerns the
existence of commutative subalgebras of the universal enveloping algebra U(g) which
would "quantise" these subalgebras of S(g).  When the Lie algebra g is simple, a general
solution of Vinberg’s problem is provided by the vertex algebra theory.  This leads to
an explicit quantisation of the shift-of-argument subalgebras in the classical types via
the symmetrisation map.


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