I discuss a method for producing a quasi–realistic inter–generational quark mass hierarchy in string models. This approach involves non–Abelian singlet states developing intermediate scale vacuum expectation values. I summarize recent investigations into string model realization of this. Talk presented at QCD98, Paris, France, 1–6 June 1998.

In this paper we develop the obstruction theory for lifting complexes, up to quasi-isomorphism, to derived categories of flat nilpotent deformations of abelian categories. As a particular case we also obtain the corresponding obstruction theory for lifting of objects in terms of Yoneda Extgroups. In appendix we prove the existence of miniversal derived deformations of complexes.

We investigate crossed products of Cuntz algebras by quasi-free actions of abelian groups. We prove that our algebras are AF-embeddable when actions satisfy a certain condition. We also give a necessary and sufficient condition that our algebras become simple and purely infinite, and consequently our algebras are either purely infinite or AF-embeddable when they are simple.

We give a completely algebraic proof of the Bogomolov-Tian-Todorov theorem. More precisely, we shall prove that if X is a smooth projective variety with trivial canonical bundle defined over an algebraically closed field of characteristic 0, then the L∞-algebra governing infinitesimal deformations of X is quasi-isomorphic to an abelian differential graded Lie algebra.

In the present paper I show that one can recover much of the inertia structure of (quasi) divisors of a function field K|k over an algebraically closed base field k from the maximal pro-` abelian-by-central Galois theory of K. The results play a central role in the birational anabelian geometry and related questions.

In this paper, we introduce the notion of Grothendieck enriched categories for over a sufficiently nice monoidal category $$\mathcal {V}$$ , generalizing classical categories. Then establish Gabriel-Popescu type theorem We also prove that property being is preserved under change base by right adjoint functor. particular, if take as complexes abelian groups, obtain dg As an application main resu...

We show that the Hamiltonian dynamics of the self-interacting, abelian p-form theory in D = 2p+ 2 dimensional space-time gives rise to the quasi-local structure. Roughly speaking, it means that the field energy is localized but on closed 2p-dimensional surfaces (quasi-localised). From the mathematical point of view this approach is implied by the boundary value problem for the corresponding fie...

Abstract We introduce new quasi-Banach modulation spaces on locally compact abelian groups which coincide with the classical ones in Banach setting and prove their main properties. Then, we study Gabor frames quasi-lattices, significantly extending original theory introduced by Gröchenig Strohmer. These issues are key tools showing boundedness results for Kohn–Nirenberg localization operators s...

The one-dimensional electron gas exhibits spin-charge separation and power-law spectral responses to many experimentally relevant probes. Ordering in a quasi-one-dimensional system is necessarily associated with a dimensional crossover, at which sharp quasiparticle peaks, with small spectral weight, emerge from the incoherent background. Using methods of Abelian bosonization, we derive asymptot...