We investigate if every quasi-minimal group is abelian, and give a positive answer for a quasi-minimal pure group having a ∅-definable partial order with uncountable chains. We also relate two properties of a complete theory in a countable language: the existence of a quasi-minimal model and the existence of a strongly regular type. As a consequence we derive the equivalence of conjectures on c...

A non-Abelian version of the Hirota-Miwa equation is considered. In an earlier paper [Nimmo (2006) J. Phys. A: Math. Gen. 39, 5053-5065] it was shown how solutions expressed as quasideterminants could be constructed for this system by means of Darboux transformations. In this paper we discuss these solutions from a different perspective and show that the solutions are quasi-Plücker coordinates ...

If G is an abelian torsion group with generating subset G0, then by a classical result in the theory of non-unique factorizations, the block monoid B(G0) is a half-factorial monoid if each of its atoms has cross number 1. In this case, G0 is called a half-factorial set. In this note, we introduce the notion of a k-quasihalf-factorial set and show for many abelian torsion groups that G0 k-quasi-...

We discuss properties of complex algebraic orbifold groups, their characteristic varieties, and their abelian covers. In particular, we deal with the question of (quasi)-projectivity of orbifold groups. We also prove a structure theorem for the variety of characters of normalcrossing quasi-projective orbifold groups. Finally, we extend Sakuma’s formula for the first Betti number of abelian cove...

The amplitude for emitting n bosons factorizes into the product of n singleboson emission amplitudes, if the source is energetic and abelian. If it is energetic but non-abelian, the amplitude is given by a sum of factorized quasi-particle amplitudes. A quasi-particle is made up of an arbitrary number of bosons, but couples to the source like a single one. Factorization is related to coherence, ...

We construct a canonical compactification SQ g,K of the moduli of abelian varieties over Z[ζN , 1/N ] where ζN is a primitive Nth root of unity. It is very similar to, but slightly different from the compactification SQg,K in [N99]. Any degenerate abelian scheme on the boundary of SQ g,K is one of the (torically) stable quasi-abelian schemes introduced in [AN99], which is reduced and singular. ...

For every prime p and integer n > 3 we explicitly construct an abelian variety A/Fpn of dimension n such that for a suitable prime l the group of quasi-isogenies of A/Fpn of l-power degree is canonically a dense subgroup of the n-th Morava stabilizer group at p. We also give a variant of this result taking into account a polarization. This is motivated by the recent construction of topological ...

It is very plausible that confinement in QCD comes from linking of Wilson loops to finite-thickness vortices with magnetic fluxes corresponding to the center of the gauge group. The vortices are solitons of a gauge-invariant QCD action representing the generation of gluon mass. There are a number of other solitonic states of this action. We discuss here what we call nexus solitons, in which for...

For every prime p and integer n > 3 we explicitly construct an abelian variety A/Fpn of dimension n such that for a suitable prime l the group of quasi-isogenies of A/Fpn of l-power degree is canonically a dense subgroup of the n-th Morava stabilizer group at p. We also give a variant of this result taking into account a polarization. This is motivated by the recent construction of topological ...