ar X iv : m at h / 06 01 25 4 v 1 [ m at h . O A ] 1 1 Ja n 20 06 Rank Preserving Maps on CSL Algebras

ar X iv : m at h / 06 01 25 4 v 2 [ m at h . O A ] 2 M ar 2 00 6 Rank Preserving Maps on CSL Algebras

We give a description of a weakly continuous rank preserving map on a reflexive algebra on complex Hilbert space with commutative completely distributive subspace lattice. We show that the implementation of a rank preserving map can be described by the combination of two different types of maps. We also show that a rank preserving map can be implemented by only one type if the corresponding lat...

ar X iv : m at h / 06 01 74 3 v 1 [ m at h . SP ] 3 0 Ja n 20 06 DETERMINANTS OF ZEROTH ORDER OPERATORS

ar X iv : m at h / 04 05 17 6 v 4 [ m at h . R T ] 1 6 Ju n 20 06 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 / 01 06 13 1 v 1 [ m at h . O A ] 1 5 Ju n 20 01 INJECTIVE ENVELOPES OF C ∗ - ALGEBRAS AS OPERATOR MODULES

In this paper we give some characterizations of M. Hamana’s injective envelope I(A) of a C∗-algebra A in the setting of operator spaces and completely bounded maps. These characterizations lead to simplifications and generalizations of some known results concerning completely bounded projections onto C∗-algebras. We prove that I(A) is rigid for completely bounded A-module maps. This rigidity yi...

ar X iv : m at h / 06 01 47 2 v 1 [ m at h . Q A ] 1 9 Ja n 20 06 REPRESENTATIONS OF QUANTUM GROUPS DEFINED OVER COMMUTATIVE RINGS II

In this article we study the structure of highest weight modules for quantum groups defined over a commutative ring with particular emphasis on the structure theory for invariant bilinear forms on these modules.