We briefly review the classical construction of the Cheeger-Simons characters, the Deligne cohomology groups and the differential K-theory groups, which are representatives of the absolute differential refinement of the ...

In this work, we have constructed more general versions of differential integration maps in differential cohomology theories. Among the obtained versions we can mention the integration with compact supports, the integration ...

Let be a Lie–Rinehart algebra such that L is S-projective and let U be its universal enveloping algebra. In this paper we present a spectral sequence which converges to the Hochschild cohomology of U with values on a ...

We compute the multiplicative structure in the Hochschild cohomology ring of a differential operators ring and the cap product of Hochschild cohomology on the Hochschild homology.

In this thesis, we study three important topics. The first one provides an axiomatic framework to differential cohomology on maps of pairs of topological spaces, introducing the product between relative and parallel classes. ...

For a set theoretical solution of the Yang–Baxter equation (X, σ), we define a d.g. bialgebra B = B(X, σ), containing the semigroup algebra A = k{X}/xy = zt : σ(x, y) = (z,t) , such that k ⊗A B ⊗A k and HomA−A(B, k) are ...

We describe the space of central extensions of the associative algebra Ψn of formal pseudo-differential symbols in n≥1 independent variables using Hochschild (co)homology groups: we prove that the first Hochschild (co)homology ...

We describe the space of central extensions of the associative algebra Ψn of formal pseudo-differential symbols in n≥1 independent variables using Hochschild (co)homology groups: we prove that the first Hochschild (co)homology ...

One way of formulating De Rham's theorem' smoothly in parameters' is to construct the De Rham cohomology groups, and the (duals of the) singular homology groups as sheaves of smooth modules over the space of parameters, ...

Let R be the homogeneous coordinate ring of a smooth projective variety X over a field k of characteristic 0. We calculate the K-theory of R in terms of the geometry of the projective embedding of X. In particular, if X ...