The Hochschild and (cotriple) cyclic homologies of crossed modules of (notnecessarily-unital) associative algebras are investigated. Wodzicki’s excision theorem is extended for inclusion crossed modules in the category of crossed modules of algebras. The cyclic and cotriple cyclic homologies of crossed modules are compared in terms of long exact homology sequence, generalising the relative cycl...

In their recent proof [2] of Schapira-Schneider’s conjecture [19], Bressler-Nest-Tsygan construct a (generalized) Chern character from the Ktheory of perfect complexes to the negative cyclic homology HC− ∗ (A) of a sheaf of algebras A on a topological space. The first aim of this paper is to show how to construct a (classical) Chern character defined on the Grothendieck group of perfect complex...

In this article, the cyclic homology theory of formal deformation quantizations of the convolution algebra associated to a proper étale Lie groupoid is studied. We compute the Hochschild cohomology of the convolution algebra and express it in terms of alternating multi-vector fields on the associated inertia groupoid. We introduce a noncommutative Poisson homology whose computation enables us t...