Isomorphisms of deformations and quantizations of Kleinian singularities

Simone Castellan (University of Glasgow)

Wednesday 7th February 16:00-17:00 Maths 110


Given a non-commutative algebra Q and its semiclassical limit A, an intriguing question has always been “Do the properties of Q always reflect the (Poisson) properties

of A?”. Of particular interest is the behaviour of automorphisms. The most famous example is the Belov Kanel-Kontsevich Conjecture, which predicts that the group of

automorphisms of the nth-Weyl algebra An is isomorphic to the group of Poisson automorphisms of the polynomial algebra C[x1, . . . , x2n]. In this talk, I will present my work

on a problem similar to the BKK Conjecture. Take a symplectic quotient singularity; the parameter spaces of filtered deformations and the parameter space of filtered quantizations

coincide. Do the Poisson isomorphisms between the deformations coincide with the automorphisms between the quantizations? The answer is affirmative in the case of Kleinian

singularities of type A and D.

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