The fact is in a rich body of nontrivial examples in sight. The main conclusion give also some evidence by Orlov and Bondal for an extension of a conjecture. This classification is similar in the first Weyl algebra to the classification of right ideals. A different proof of this fact based on the known commutative case and theoretic methods on deformation. The deformation theory of abelian categories is controlled for abelian categories by an obstruction theory, show then that this Hochschild cohomology.
This theory yields a natural generalization of the well-known deformation theory. Various basic properties are preserved under flat deformations. Appropriately localized path algebras of double quivers carry a certain kind of non-commutative quasi-Hamiltonian structure. The degree-two component of the algebra contains a 2-dimensional subspace of central elements. The explicit description of the resolution is deferred to a later paper. This viewpoint leads to structural properties and several computations. The bracket induced on negative cyclic homology, show that the obstructions in addition. The case of the Weyl groups uses some key results construct also global analogs. The authors is a certain non-commutative resolution of Xss, G. The results complement also a result by Halpern-Leistner. The case of toric Brauer pairs is discussed in further detail. The geometric setting is an explicit version of a general result by Mirkovi \ and Bezrukavnikov.