ar X iv : m at h / 07 02 79 3 v 1 [ m at h . R A ] 2 6 Fe b 20 07 INJECTIVE REPRESENTATIONS OF INFINITE QUIVERS . APPLICATIONS

ar X iv : m at h / 06 12 20 6 v 3 [ m at h . R T ] 1 6 Fe b 20 07 CURRENT ALGEBRAS , HIGHEST WEIGHT CATEGORIES AND QUIVERS

We study the category of graded finite-dimensional representations of the polynomial current algebra associated to a simple Lie algebra. We prove that the category has enough injectives and compute the graded character of the injective envelopes of the simple objects as well as extensions betweeen simple objects. The simple objects in the category are parametized by the affine weight lattice. W...

ar X iv : m at h - ph / 0 20 20 30 v 1 2 1 Fe b 20 02 On entanglement of states and quantum correlations ∗

In this paper we present the novel qualities of entanglement of formation for general (so also infinite dimensional) quantum systems and we introduce the notion of coefficient of quantum correlations. Our presentation stems from rigorous description of entanglement of formation.

ar X iv : m at h / 06 02 37 1 v 1 [ m at h . A G ] 1 7 Fe b 20 06 Braid Monodromy of Hypersurface Singularities

ar X iv : m at h / 01 02 20 3 v 1 [ m at h . A G ] 2 6 Fe b 20 01 THE T 1 - LIFTING THEOREM IN POSITIVE CHARACTERISTIC STEFAN

Replacing symmetric powers by divided powers and working over Witt vectors instead of ground fields, I generalize Kawamatas T -lifting theorem to characteristic p > 0. Combined with the work of Deligne–Illusie on degeneration of the Hodge–de Rham spectral sequences, this gives unobstructedness for certain Calabi–Yau varieties with free crystalline cohomology modules.

ar X iv : m at h / 99 02 08 6 v 1 [ m at h . SP ] 1 4 Fe b 19 99 THE REDUCED WAVE EQUATION IN LAYERED MATERIALS