Quantized Quiver Varieties
نویسنده
چکیده
1.1. General formalism and basic examples. Let A = ⊕ i>0Ai be a graded algebra equipped with a Poisson bracket {·, ·} that has degree −1 because {Ai, Aj} ⊂ Ai+j−1. By a quantization of A one means a pair (A, ι), where • A is a filtered associative unital algebra A = ∪ i>0 A6i. • ι : grA → A is an isomorphism of graded Poisson algebras. Recall that grA := ⊕ i>0 A6i/A6i−1 is a graded algebra. Thanks to the presence of ι, this algebra is commutative meaning that [A6i,A6j] ⊂ A6i+j−1. We define the bracket on grA by {a+A6i−1, b+A6j−1} := [a, b] +A6i+j−2. Let us consider some examples.
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