Related papers: \v{C}ech cocycles for quantum principal bundles

Associated to a differential character is an integral cohomology class, referred to as the characteristic class, and a closed differential form, referred to as the curvature. The characteristic class and curvature are equal in de Rham…

In this work, the notion of a quantum inverse semigroup is introduced as a linearized generalization of inverse semigroups. Beyond the algebra of an inverse semigroup, which is the natural example of a quantum inverse semigroup, several…

We use compactifications of C*-algebras to introduce noncommutative coarse geometry. We transfer a noncommutative coarse structure on a C*-algebra with an action of a locally compact Abelian group by translations to Rieffel deformations and…

In [1] we introduced the concept of structured space, which is a topological space that locally resembles some algebraic structures. In [2] we proceeded the study of these spaces, developing two cohomology theories. The aim of this paper is…

We give a systematic description of the cyclic cohomology theory of Hopf algebroids in terms of its associated category of modules. Then we introduce a dual cyclic homology theory by applying cyclic duality to the underlying cocyclic…

Localisation is an important technique in ring theory and yields the construction of various rings of quotients. Colocalisation in comodule categories has been investigated by some authors where the colocalised coalgebra turned out to be a…

In this paper, we give a combinatorial formula for the \v{C}ech cocycles representing the power sums of the Chern roots of a holomorphic vector bundle over a complex manifold. By an observation motivation by author's previous paper, we also…

We continue the development of the homological theory of quantum general linear groups previously considered by the first author. The development is used to transfer information to the representation theory of quantised Schur algebras. The…

In this article, we give a class of examples of compact quantum groups and unitary 2-cocycles on them, such that the twisted quantum groups are non-compact, but still locally compact quantum groups (in the sense of Kustermans and Vaes).…

For a commutative algebra the shuffle product is a morphism of complexes. We generalize this result to the quantum shuffle product, associated to a class of non-commutative algebras (for example all the Hopf algebras). As a first…

We study a noncommutative version of the infinitesimal site of Grothendieck. A theorem of Grothendieck establishes that the cohomology of the structure sheaf on the infinitesimal topology of a scheme of characteristic zero is de Rham…

The relationship between comodules of a coring and flat connections is reviewed. In particular we specialise to corings which are built on a tensor product of algebra and a coalgebra. Such corings are in one-to-one correspondence with…

In this paper, we study equivariant real cycle class maps for group actions on real schemes, with a view toward Witt-sheaf characteristic classes. The cycle class maps take values in singular cohomology of the real points of the quotient…

It is well--known that if one is given a principal $G$--bundle with a principal connection, then for every unitary finite--dimensional linear representation of $G$ one can induce a linear connection and a Hermitian structure on the…

In this paper we obtain a description of the Grothendieck group of complex vector bundles over the classifying space of a p-local finite group in terms of representation rings of subgroups of its Sylow. We also prove a stable elements…

The sheaf theoretic description of non-locality and contextuality by Abramsky and Brandenburger sets the ground for a topological study of these peculiar features of quantum mechanics. This viewpoint has been recently developed thanks to…

A new quantization of groupoids under the name of \times-Hopf coalgebras is introduced. We develop a Hopf cyclic theory with coefficients in stable-anti-Yetter-Drinfeld modules for \times-Hopf coalgebras. We use \times-Hopf coalgebras to…

We construct relative and global Euler sequences of a module. We apply it to prove some acyclicity results of the Koszul complex of a module and to compute the cohomology of the sheaves of (relative and absolute) differential $p$-forms of a…

In this article, we investigate Hecke modifications of vector bundles on a smooth projective curve $X$ defined over an arbitrary field. We obtain structural results that allow us to reduce the classification problem of Hecke modifications…

We extend the notion of monogenic extension to the noncommutative setting, and we study the Hochschild cohomology ring of such an extension. As an aplication we complete the computation of the cohomology ring of the rank one Hopf algebras…