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 …

We consider the action of Vect Pol (R) by Lie derivative on the spaces of symbols of
differential operators. We study the deformations of this action that become trivial once …

We consider the action of the Lie algebra of polynomial vector fields, vect (1), by the Lie
derivative on the space of symbols Sβn=⨁ j= 0nFβ− j. We study the deformations of this …

Supertransvectants, cohomology, and deformations | Journal of Mathematical Physics | AIP
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Abstract We consider the sl\,(2)-module structure on the spaces of symbols of differential
operators acting on the spaces of weighted densities. We compute the necessary and …

In 1928, at the IMC, Veblen posed the problem: classify invariant differential operators
between spaces of “natural objects”(in modern terms: either tensor fields, or jets) over a real …

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) …

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 …

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 …