211 research outputs found
Deforming the Lie algebra of vector fields on inside the Poisson algebra on
We study deformations of the standard embedding of the Lie algebra
\Vect(S^1) of smooth vector fields on the circle, into the Lie algebra of
functions on the cotangent bundle (with respect to the Poisson
bracket). We consider two analogous but different problems: (a) formal
deformations of the standard embedding of \Vect(S^1) into the Lie algebra of
functions on \dot T^*S^1:=T^*S^1\setminusS^1 which are Laurent polynomials on
fibers, and (b) polynomial deformations of the \Vect(S^1) subalgebra inside
the Lie algebra of formal Laurent series on .Comment: 19 pages, LaTe
Conformally invariant differential operators on tensor densities
Let be the space of tensor densities on of
degree (or, equivalently, of conformal densities of degree
) considered as a module over the Lie algebra . We
classify -invariant bilinear differential operators from to~. The classification of linear
-invariant differential operators from to
already known in the literature is obtained in a different
manner.Comment: 11 pages, LaTe
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