ar X iv : m at h / 04 05 08 1 v 1 [ m at h . L O ] 5 M ay 2 00 4 Preserving Preservation

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 / 05 05 08 2 v 1 [ m at h . R A ] 5 M ay 2 00 5 FINITE - DIMENSIONAL ALGEBRAS AND QUIVERS

This is an overview article on finite-dimensional algebras and quivers, written for the Encyclopedia of Mathematical Physics. We cover path algebras, Ringel-Hall algebras and the quiver varieties of Lusztig and Nakajima.

ar X iv : h ep - p h / 04 05 11 9 v 1 1 3 M ay 2 00 4 The Lorentz and CPT violating effects on the charged

ar X iv : h ep - p h / 04 05 03 5 v 1 5 M ay 2 00 4 Determination of the mass of the ΛΛ dibaryon by the method of QCD sum rules

ar X iv : m at h / 05 04 08 2 v 4 [ m at h . D G ] 1 5 A pr 2 00 6 COMPLETE PROJECTIVE CONNECTIONS

The first examples of complete projective connections are uncovered: on surfaces, normal projective connections whose geodesics are all closed and embedded are complete. On manifolds of any dimension, normal projective connections induced from complete affine connections with slowly decaying positive Ricci curvature are complete.