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 M be either a projective manifold (M, Π) or a pseudo-Riemannian manifold (M, g). We
extend, intrinsically, the projective/conformal Schwarzian derivatives we have introduced …

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 …

The space Dλ¯; μ, where λ¯=(λ1,…, λm), of m-ary differential operators acting on weighted
densities is a (m+ 1)-parameter family of modules over the Lie algebra of vector fields. For …

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 …

Let Vect ($\mathbb {R} $) be the Lie algebra of smooth vector fields on $\mathbb {R} $ and
$\mathbb {F} _ {\lambda} $ be the space of $\lambda $-densities on $\mathbb {R} $. Vect …

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 …

We consider the spaces $\mathcal {F} _\mu $ of polynomial $\mu $-densities on the line as
$\mathfrak {sl}(2) $-modules and then we compute the cohomological spaces $\mathrm {H} …

We compute the first cohomology of the ortosymplectic Lie superalgebra osp (1| 2) on the (1,
1)-dimensional real superspace with coefficients in the superspace Dλ, ν; µ of bilinear …