ar X iv : m at h / 04 11 35 1 v 2 [ m at h . A T ] 1 7 N ov 2 00 4 POINCARÉ SUBMERSIONS

ar X iv : m at h / 04 11 06 2 v 1 [ m at h . O A ] 3 N ov 2 00 4 On automorphisms of type II Arveson systems ( probabilistic approach )

A counterexample to the conjecture that the automorphisms of an arbitrary Arveson system act transitively on its normalized units.

ar X iv : h ep - t h / 02 11 04 8 v 1 7 N ov 2 00 2 Inflation , Quantum Cosmology and the Anthropic Principle 1

ar X iv : m at h / 04 05 17 6 v 3 [ m at h . R T ] 1 7 N ov 2 00 4 QUANTIZED SYMPLECTIC OSCILLATOR ALGEBRAS OF RANK ONE

A quantized symplectic oscillator algebra of rank 1 is a PBW deformation of the smash product of the quantum plane with Uq(sl2). We study its representation theory, and in particular, its category O.

ar X iv : m at h / 04 10 61 1 v 2 [ m at h . A G ] 1 1 N ov 2 00 4 ON RATIONAL CUSPIDAL PROJECTIVE PLANE CURVES

ar X iv : m at h / 04 10 55 1 v 2 [ m at h . D G ] 1 6 N ov 2 00 4 CLASSICAL FIELD THEORY ON LIE ALGEBROIDS : VARIATIONAL ASPECTS

The variational formalism for classical field theories is extended to the setting of Lie algebroids. Given a Lagrangian function we study the problem of finding critical points of the action functional when we restrict the fields to be morphisms of Lie algebroids. In addition to the standard case, our formalism includes as particular examples the case of systems with symmetry (covariant Euler-P...