Discrete Torsion, Covering Groups and Quiver Diagrams

Covering Spaces and Discrete Groups

We have already met covering spaces in Chapter 2, where our discussion was geometric and basically limited to definitions and examples. In this chapter, we return to this topic from a more algebraic point of view, which will allow us to produce numerous examples coming from group actions and to classify all covering spaces with given base (provided the latter is “nice” enough). The main tools w...

Generalized Covering Groups and Direct Limits

quantum groups and double quiver algebras

Let Uq(g) be the Drinfeld-Jimbo quantum group, which is a deformation of the universal enveloping algebra of a finite dimensional semisimple Lie algebra g. In the generic case, i.e. the parameter q is not a root of unity, several models have been raised to realize it. For example, the Ringel-Hall algebra approach is one successful model among them, see [10, 5, 11]. The case where q is a root of...

Framed quiver moduli, cohomology, and quantum groups

Framed quiver moduli parametrize stable pairs consisting of a quiver representation and a map to a fixed graded vector space. Geometric properties and explicit realizations of framed quiver moduli for quivers without oriented cycles are derived, with emphasis on their cohomology. Their use for quantum group constructions is discussed.

Covering by Discrete and Closed Discrete Sets

Say that a cardinal number κ is small relative to the space X if κ < ∆(X), where ∆(X) is the least cardinality of a non-empty open set in X . We prove that no Baire metric space can be covered by a small number of discrete sets, and give some generalizations. We show a ZFC example of a regular Baire σ-space and a consistent example of a normal Baire Moore space which can be covered by a small n...