4 papers
Quantization of Preprojective Algebras and the Type A Rational Cherednik Algebra
Meiliang Liu, Jun Zhang, Hu Zhao
For the Jordan quiver, we construct a radial quantum trace morphism from the quantum preprojective algebra to the algebra of invariant differential operators on the Cartan subalgeb…
Shifted double Poisson structures and noncommutative Poisson extensions
Leilei Liu, Jieheng Zeng, Hu Zhao
We develop a theory of noncommutative Poisson extensions. For an augmented dg algebra \(A\), we show that any shifted double Poisson bracket on \(A\) induces a graded Lie algebra s…
Noncommutative Hamiltonian structures and quantizations on preprojective algebras
Hu Zhao
Given a noncommutative Hamiltonian space , we prove that the conjecture ``{\it quantization commutes with reduction}'' holds for . We further construct a semidirect product a…
Commutativity of Quantization and Reduction for Quiver Representations
Hu Zhao
Given a finite quiver, its double may be viewed as its non-commutative "cotangent" space, and hence is a non-commutative symplectic space. Crawley-Boevey, Etingof and Ginzburg cons…