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On (2)-relative cohomology of the Lie algebra of vector fields and differential operators
Abstract:Abstract

Let Vect(?) be the Lie algebra of smooth vector fields on ?. The space of symbols Pol(T*?) admits a non-trivial deformation (given by differential operators on weighted densities) as a Vect(?)-module that becomes trivial once the action is restricted to /></span>(2) ? Vect(?). The deformations of Pol(<i>T</i>*?), which become trivial once the action is restricted to <span class= /></span>(2) and such that the Vect(?)-action on them is expressed in terms of differential operators, are classified by the elements of the weight basis of <span class= /></span>, where <span class= /></span> denotes the differential cohomology (i.e., we consider only cochains that are given by differential operators) and where <i>D</i> <sub>λ,μ</sub> = Homdiff(<i>F</i> <sub>λ</sub>, <i>F</i> <sub>μ</sub>) is the space of differential operators acting on weighted densities. The main result of this paper is computation of this cohomology. In addition to relative cohomology, we exhibit 2-cocycles spanning <span class= /></span> and <span class= /></span>(2).</td> </tr> <tr> <td align=
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