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The main result of the paper is a natural construction of the spherical subalgebra in a symplectic reflection algebra associated with a wreath-product in terms of quantum hamiltonian reduction of an algebra of differential operators on a representation space of an extended Dynkin quiver. The existence of such a construction has been conjectured in [EG]. We also present a new approach to reflection functors and shift functors for generalized preprojective algebras and symplectic reflection algebras...
We compute Hochschild homology and cohomology of a class of generalized Weyl algebras,
introduced by V. V. Bavula in St. Petersbourg Math. Journal, 4 (1) (1999), 71-90.
Examples of such algebras are the n-th Weyl algebras, ,
primitive quotients of , and subalgebras of invariants of
these algebras under finite cyclic groups of automorphisms. We answer a question of
Bavula–Jordan (Trans. A.M.S., 353 (2) (2001), 769-794) concerning the generators of the
group of automorphisms of a generalized Weyl...
We determine the Hochschild homology and cohomology of the generalized Weyl algebras of rank one which are of ‘quantum’ type in all but a few exceptional cases.
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