ar X iv : m at h / 06 08 50 8 v 3 [ m at h . Q A ] 1 5 D ec 2 00 6 Classification of modules of the intermediate series over

ar X iv : 0 71 2 . 01 44 v 1 [ m at h . R T ] 2 D ec 2 00 7 Graded modules for Virasoro - like algebra ∗

In this paper, we consider the classification of irreducible Zand Z2-graded modules with finite dimensional homogeneous subspaces over the Virasoro-like algebra. We first prove that such a module is a uniformly bounded module or a generalized highest weight module. Then we determine all generalized highest weight irreducible modules. As a consequence, we also determine all the modules with nonz...

ar X iv : h ep - t h / 06 12 12 8 v 1 1 3 D ec 2 00 6 Riemannian Geometry of Noncommutative Surfaces

ar X iv : m at h / 01 04 17 8 v 1 [ m at h . N T ] 1 8 A pr 2 00 1 Arithmetic theory of q - difference equations

Part II. p-adic methods §3. Considerations on the differential case §4. Introduction to p-adic q-difference modules 4.1. p-adic estimates of q-binomials 4.2. The Gauss norm and the invariant χv(M) 4.3. q-analogue of the Dwork-Frobenius theorem §5. p-adic criteria for unipotent reduction 5.1. q-difference modules having unipotent reduction modulo ̟v 5.2. q-difference modules having unipotent redu...

ar X iv : m at h / 98 08 06 5 v 1 [ m at h . Q A ] 1 4 A ug 1 99 8 QUANTUM DETERMINANTS AND QUASIDETERMINANTS

ar X iv : m at h / 03 06 08 8 v 1 [ m at h . A T ] 5 J un 2 00 3 Diagrams and the second homotopy group

We use Klyachko’s methods [2,3,4,6] to prove that, if a 1–cell and a 2–cell are added to a complex with torsion-free fundamental group, and with the 2–cell attached by an amenable t–shape, then π2 changes by extension of scalars. We also prove that the normal closure of the attaching word contains no words of smaller complexity. AMS Classification 57M20, 57Q05; 20E22, 20F05