HOCHSCHIELD HOMOLOGIES IN ALGEBRAS OF DIFFERENTIAL OPERATORS AND GENERALIZED POISSON STRUCTURES

Abstract

The work has been devoted to the investigation of applying Poisson cohomologies to the problems of the classification of the degenerate Poisson structures and calculation of the Hochschield homologies in the algebras of the differential operators acting in the sections of the vector separation. The formal classification of the Poisson structures in the points where their rank is equal to zero has been obtained. The normal forms of the degenerate Poisson structures in the terms of the spectral subsequence converging to the Poisson cohomologies of the Poisson structure growth have been described. The spectral subsequence for calculating Hochschield homologies in the algebras of differential operators acting in the sections of the vector separations have been constructed. The calculation of the term E*99P*99,*99q*001 of the given subsequence has been reduced to the calculation of the Poisson homologies. Its results can find application in the differential geometry, quantum theory of field, mathematical physics. The different methods of the differential geometry, homological algebra and theory of differential equations were used at proof of the basis theoremsAvailable from VNTIC / VNTIC - Scientific & Technical Information Centre of RussiaSIGLERURussian Federatio