Coverings in the representation theory of algebras were introduced for the Auslander-Reiten quiver of a representation finite algebra in [15] and later for finite dimensional algebras in [2, 7, 11]. The best understood class of covering functors is that of Galois covering functors F : A → B determined by the action of a group of automorphisms of A. In this work we introduce the balanced coverin...

let $a$ be a nite dimensional $k-$algebra and $r$ be a locally bounded category such that $r rightarrow r/g = a$ is a galois covering dened by the action of a torsion-free group of automorphisms of $r$. following [30], we provide criteria on the convex subcategories of a strongly simply connected category r in order to be a cycle- nite category and describe the module category of $a$. we pro...

We study primary and secondary invariants of leafwise Dirac operators on foliated bundles. Given such an operator, we begin by considering the associated regular self-adjoint operator Dm on the maximal Connes-Skandalis Hilbert module and explain how the functional calculus of Dm encodes both the leafwise calculus and the monodromy calculus in the corresponding von Neumann algebras. When the fol...

This article is the second part of a series three articles, in which we develop higher covering theory racks and quandles. project rooted M. Eisermann’s work on quandle coverings, categorical perspective brought to subject by V. Even, who characterizes coverings as those surjections are categorically central, relatively trivial We extend this applying techniques from Galois theory, sense G. Jan...

Applying geometric methods of 2-dimensional cell complex theory, we construct a Galois covering bimodule problem satisfying some structure, triangularity and finiteness conditions in order to describe the objects finite representation type. Each admitted A is endowed with quasi multiplicative basis. The main result shows that for from considered class having restrictions schurian universal A', ...

Abstract The theory of R. Crowell on derived modules is approached within the non-commutative differential modules. We also seek analogies to cotangent complex from differentials in commutative ring setting. Finally, we give examples motivated Galois coverings curves.

Higher dimensional central extensions of groups were introduced by G. Janelidze as particular instances of the abstract notion of covering morphism from categorical Galois theory. More recently, the notion has been extended to and studied in arbitrary semi-abelian categories. Here, we further extend the scope to exact Mal’tsev categories and beyond. For this, we consider conditions on a Galois ...

We study the existence of L holomorphic sections of invariant line bundles over Galois coverings of Zariski open sets in Moishezon manilolds. We show that the von Neuman dimension of the space of L holomorphic sections is bounded below under reasonable curvature conditions. We also give criteria for a a compact complex space with isolated singularities and some related strongly pseudoconcave ma...

Let $A$ be a nite dimensional $k-$algebra and $R$ be a locally bounded category such that $R rightarrow R/G = A$ is a Galois covering dened by the action of a torsion-free group of automorphisms of $R$. Following [30], we provide criteria on the convex subcategories of a strongly simply connected category R in order to be a cycle- nite category and describe the module category of $A$. We p...