Simplicity of the canonical quantization of a conic symplectic singularity (Losev’s conjecture)

Prove that for any conic symplectic singularity X, its canonical quantization U (as defined in Losev’s classification of quantizations) is a simple ring, i.e., has no proper two-sided ideals.

Background

Quantizations U of a conic symplectic singularity X are filtered algebras whose associated graded Poisson algebra is the coordinate ring C[X]. Losev’s classification provides a canonical quantization among these. The survey presents Losev’s conjecture asserting the simplicity of this canonical quantization, and notes that in the special case when X has Q-factorial terminal singularities, the unique quantization U would then be simple.

Establishing simplicity would parallel the simple-ring behavior of Weyl algebras and would open the door to extending Stafford’s module-structure results to broader classes of quantized symplectic singularities.