Homology of algebras of families of pseudodifferential operators. (Q1421838)

The authors study the Hochschild homology of certain algebras of complete symbols, that is, the quotient of the algebra of all pseudodifferential operators by the ideal of regularizing (or order \(-\infty\)) operators. The Hochschild, cyclic, and periodic cyclic homology groups of algebras of families of Laurent complete symbols on manifolds with corners are computed. Some applications, in particular, to the explicit description of the space of traces on algebras of complete symbols are also given.