ar X iv : m at h / 04 09 16 2 v 1 [ m at h . R A ] 9 S ep 2 00 4 RESOLUTIONS OVER KOSZUL ALGEBRAS

ar X iv : m at h / 04 09 02 9 v 1 [ m at h . A G ] 2 S ep 2 00 4 ACM BUNDLES ON GENERAL HYPERSURFACES IN P 5 OF LOW DEGREE

In this paper we show that on a general hypersurface of degree r = 3, 4, 5, 6 in P 5 a rank 2 vector bundle E splits if and only if h 1 E(n) = h 2 E(n) = 0 for all n ∈ Z. Similar results for r = 1, 2 were obtained in [15], [16] and [1].

ar X iv : h ep - p h / 02 04 09 8 v 1 9 A pr 2 00 2 GUT GENEALOGIES FOR SUSY SEESAW HIGGS

We discuss the embedding of R-Parity preserving Minimal Left Right Supersym-metric models into Pati-Salam and SO(10) GUTs.

ar X iv : h ep - p h / 04 05 03 9 v 1 5 M ay 2 00 4 η , η ′ → π + π − γ with coupled channels

ar X iv : m at h / 02 06 04 1 v 2 [ m at h . FA ] 9 S ep 2 00 2 Abstract harmonic analysis , homological algebra , and operator spaces

harmonic analysis, homological algebra, and operator spaces

ar X iv : h ep - t h / 04 09 01 2 v 1 1 S ep 2 00 4 Construction of θ - Poincaré Algebras and their Invariants on M θ

In the present paper we construct deformations of the Poincaré algebra as representations on a noncommutative spacetime with canonical commutation relations. These deformations are obtained by solving a set of conditions by an appropriate ansatz for the deformed Lorentz generator. They turn out to be Hopf algebras of quantum universal enveloping algebra type with nontrivial antipodes. In order ...