Abstract Following Feigin and Fuchs, we compute the first cohomology of the Lie
superalgebra K (1) of contact vector fields on the (1, 1)-dimensional real or complex …

The main topic of this paper is two-fold. First, we compute the first relative cohomology group
of the Lie algebra of smooth vector fields on the projective line, Vect (ℝℙ1), with coefficients …

The Bol operators are unary differential operators between spaces of weighted densities on
the 1-dimensional manifold invariant under projective transformations of the manifold. On …

Let Vect (ℝ) be the Lie algebra of smooth vector fields on ℝ. The space of symbols Pol (T* ℝ)
admits a non-trivial deformation (given by differential operators on weighted densities) as a …

ON aff(1)-RELATIVE COHOMOLOGY OF THE LIE ALGEBRA OF VECTOR FIELDS ON
WEIGHTED DENSITIES ON R Page 1 ON aff(1)-RELATIVE COHOMOLOGY OF THE LIE …

Abstract We consider the 1| 2-dimensional real superspace R 1| 2 endowed with its standard
contact structure defined by the 1-form α. The conformal Lie superalgebra K (2) acts on R 1 …

In this paper, we denote the Lie algebra of smooth vector fields on RP 1 by V (RP 1). This
paper focuses on two parts. In the beginning, we determine the cohomology space of aff (1) …

Abstract Over the (1, 2)-dimensional real superspace R 1| 2. We compute the second aff (2|
1)-relative cohomology space of K (2) with coefficients in the module of λ-densities F λ 2 on …

Let Vect (ℝ) be the Lie algebra of smooth vector fields on ℝ and λ, μ; ν:= Hom diff (ℱ λ⊗ ℱ μ,
ℱ ν) be the space of bilinear differential operators acting on weighted densities. In this …

We consider the 1| 1-dimensional real superspace ℝ 1| 1 endowed with its standard contact
structure defined by the 1-form α. The conformal Lie superalgebra 𝒦 (1) acts on ℝ 1| 1 as the …