2,980 research outputs found
On sl(2)-equivariant quantizations
By computing certain cohomology of Vect(M) of smooth vector fields we prove
that on 1-dimensional manifolds M there is no quantization map intertwining the
action of non-projective embeddings of the Lie algebra sl(2) into the Lie
algebra Vect(M). Contrariwise, for projective embeddings sl(2)-equivariant
quantization exists.Comment: 09 pages, LaTeX2e, no figures; to appear in Journal of Nonlinear
Mathematical Physic
Cohomology of groups of diffeomorphims related to the modules of differential operators on a smooth manifold
Let be a manifold and be the cotangent bundle. We introduce a
1-cocycle on the group of diffeomorphisms of with values in the space of
linear differential operators acting on When is the
-dimensional sphere, , we use this 1-cocycle to compute the
first-cohomology group of the group of diffeomorphisms of , with
coefficients in the space of linear differential operators acting on
contravariant tensor fields.Comment: arxiv version is already officia
Decomposition of symmetric tensor fields in the presence of a flat contact projective structure
Let be an odd-dimensional Euclidean space endowed with a contact 1-form
. We investigate the space of symmetric contravariant tensor fields on
as a module over the Lie algebra of contact vector fields, i.e. over the
Lie subalgebra made up by those vector fields that preserve the contact
structure. If we consider symmetric tensor fields with coefficients in tensor
densities, the vertical cotangent lift of contact form is a contact
invariant operator. We also extend the classical contact Hamiltonian to the
space of symmetric density valued tensor fields. This generalized Hamiltonian
operator on the symbol space is invariant with respect to the action of the
projective contact algebra . The preceding invariant operators lead
to a decomposition of the symbol space (expect for some critical density
weights), which generalizes a splitting proposed by V. Ovsienko
Deformations of modules of differential forms
We study non-trivial deformations of the natural action of the Lie algebra
on the space of differential forms on . We calculate abstractions for integrability of infinitesimal
multi-parameter deformations and determine the commutative associative algebra
corresponding to the miniversal deformation in the sense of \cite{ff}.Comment: Published by JNMP at http://www.sm.luth.se/math/JNM
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