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)
There are nontrivial dualities and parallels between polynomial algebras and the Grassmann algebras. This paper is an attempt to look at the Grassmann algebras at the angle of the Jacobian conjecture for polynomial algebras (which is the ques-tion/conjecture about the Jacobian set – the set of all algebra endomorphisms of a polynomial algebra with 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)