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Hochschild homology of the algebra of $$H$$-differential operators. (English. Russian original) Zbl 0965.17012
Mosc. Univ. Math. Bull. 50, No. 4, 18-23 (1995); translation from Vestn. Mosk. Univ., Ser. I 1995, No. 4, 19-25 (1995).
Summary: The algebra of differential operators that acts in vector bundles and its subalgebras that have a commutative ring of symbols are considered. Such algebras are called algebras of differential operators, since they are associated with algebra bundles of the given model $$A\subset \text{End} (\mathbb{R}^n)$$, $$H\subset A$$. The commutativity of the algebra of symbols allows one to introduce the Poisson structure in the usual way, which is used for computation of the first term of the spectral sequence converging to the Hochschild homology of the given algebra of differential operators.
##### MSC:
 17B55 Homological methods in Lie (super)algebras 19D55 $$K$$-theory and homology; cyclic homology and cohomology