32 research outputs found
sl(2)-Trivial Deformations of Vect_{Pol}(R)-Modules of Symbols
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 restricted to sl(2). Necessary and sufficient
conditions for integrability of infinitesimal deformations are given.Comment: This is a contribution to the Special Issue on Deformation
Quantization, published in SIGMA (Symmetry, Integrability and Geometry:
Methods and Applications) at http://www.emis.de/journals/SIGMA
Second cohomology space of acting on the space of -ary differential operators on
We consider the spaces of polynomial -densities on the
line as -modules and then we compute the cohomological spaces
, where ,
and is the space of
-ary differential operators from
to .Comment: 15 page
The spaces for some weight modules
We entirely compute the cohomology for a natural and large class of
modules . We study the restriction to the
cohomology of and apply our results to the module
of differential operators on the super circle,
acting on densities
Cohomology of acting on linear differential operators on the supercircle $S^{1|1}
We compute the first cohomology spaces
() of the Lie superalgebra with
coefficients in the superspace of linear
differential operators acting on weighted densities on the supercircle
. The structure of these spaces was conjectured in \cite{gmo}. In
fact, we prove here that the situation is a little bit more complicated. (To
appear in LMP.
The Binary Invariant Differential Operators on Weighted Densities on the superspace and Cohomology
Over the -dimensional real superspace, , we classify
-invariant binary differential operators acting on the
superspaces of weighted densities, where is the Lie
superalgebra of contact vector fields. This result allows us to compute the
first differential cohomology of %the Lie superalgebra with
coefficients in the superspace of linear differential operators acting on the
superspaces of weighted densities--a superisation of a result by Feigin and
Fuchs. We explicitly give 1-cocycles spanning these cohomology spaces
Cohomology of acting on the space of bilinear differential operators on the superspace
We compute the first cohomology of the ortosymplectic Lie superalgebra
on the (1,1)-dimensional real superspace with
coefficients in the superspace of bilinear
differential operators acting on weighted densities. This work is the simplest
superization of a result by Bouarroudj [Cohomology of the vector fields Lie
algebras on acting on bilinear differential operators,
International Journal of Geometric Methods in Modern Physics
(2005), {\bf 2}; N 1, 23-40]