Vladimir V. Bavula

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We present solutions to isomorphism problems for various generalized Weyl algebras, including deformations of type-A Kleinian singularities 14] and the algebras similar to U(sl 2) introduced in 31]. For the former, we generalize results of Dixmier 11, 12] on the rst Weyl algebra and the minimal primitive factors of U(sl 2) by nding sets of generators for(More)
For the ring of differential operators on a smooth affine algebraic variety X over a field of characteristic zero a finite set of algebra generators and a finite set of defining relations are found explicitly. As a consequence, a finite set of generators and a finite set of defining relations are given for the module Der K (O(X)) of derivations on the(More)
Let d be the left homological dimension or weak dimension. In the present paper we give for a large class of algebras the answer to the question: when the dimension of the tensor product of algebras is the sum of dimensions of the multiples, Tensor d-minimal algebras are introduced and it is proved that a large class of algebras are tensor d-minimal(More)
Let A n be the n'th Weyl algebra and P m be a polynomial algebra in m variables over a field K of characteristic zero. The following characterization of the algebras {A n ⊗ P m } is proved: an algebra A admits a finite set δ 1 ,. .. , δ s of commuting locally nilpotent derivations with generic kernels and ∩ s i=1 ker(δ i) = K iff A ≃ A n ⊗ P m for some n(More)
Let K be a perfect field of characteristic p > 0, A 1 := Kx, ∂ | ∂x − x∂ = 1 be the first Weyl algebra and Z := K[X := x p , Y := ∂ p ] be its centre. It is proved that (i) the restriction map res : Aut K (A 1) → Aut K (Z), σ → σ| Z , is a monomorphism with im(res) = Γ := {τ ∈ Aut K (Z) | J (τ) = 1} where J (τ) is the Jacobian of τ (note that Aut K (Z) = K(More)
We study in detail the algebra Sn in the title which is an algebra obtained from a polynomial algebra Pn in n variables by adding commuting, left (but not two-sided) inverses of the canonical generators of Pn. The algebra Sn is non-commutative and neither left nor right Noetherian but the set of its ideals satisfies the a.c.c., and the ideals commute. It is(More)