We construct the intermediate coverings of cluster-tilted algebras by defining the generalized cluster categories. These generalized cluster categories are Calabi-Yau triangulated categories with fraction CY-dimension and have also cluster tilting objects (subcategories). Furthermore we study the representations of these intermediate coverings of cluster-tilted algebras.

In this paper we are interested in the following question: what is the smallest number of circuits, s(n,r), that is sufficient to determine every uniform oriented matroid of rank r on n elements? We shall give different upper bounds for s(n,r) by using special coverings called connected coverings. (~) 1998 Elsevier Science B.V. All rights reserved

Thin coverings are a method of constructing graded-simple modules from simple (ungraded) modules. After a general discussion, we classify the thin coverings of (quasifinite) simple modules over associative algebras graded by finite abelian groups. The classification uses the representation theory of cyclotomic quantum tori. We close with an application to representations of multiloop Lie algebras.

We identify the normal subgroups of the orientation preserving subgroup [3, 5, 3] of the Coxeter group [3, 5, 3], with the factor group isomorphic to PSL2(Fq) with particular congruence subgroups of an arithmetic subgroup of PSL2(C) derived from a quaternion algebra over a quartic field. 1 Motivation – Hurwitz groups and HurwitzMacbeath surfaces It is a well known fact that up to isomorphy, the...

Branched coverings relate closed, orientable 3-manifolds to links in S, and open, orientable 3-manifolds to strings in S r T , where T is a compact, totally disconnected tamely embedded subset of S. Here we give the foundations of this last relationship. We introduce Fox theory of branched coverings and state the main theorems. We give examples to illustrate the theorems.

In this paper we use Janelidze’s approach to the classical theory of topological coverings via categorical Galois theory to study coverings in categories of relational algebras. Moreover, we present characterizations of effective descent morphisms in the categories of M ordered sets and of multi-ordered sets.

In this paper, uniform designs are constructed based on nearly U-type designs and the discrete discrepancy. The link between such uniform designs and resolvable packings and coverings in combinatorial design theory is developed. Through resolvable packings and coverings without identical parallel classes, many infinite classes of new uniform designs are then produced.

A stapled sequence is a set of consecutive positive integers such that no one of them is relatively prime with all of the others. The problem of existence and construction of stapled sequences of length N was extensively studied for over 60 years by Pillai, Evans, Brauer, Harborth, Erdös and others. Sivasankaranarayana, Szekeres and Pillai proved that no stapled sequences exist for any N < 17. ...