ar X iv : m at h / 04 06 31 1 v 1 [ m at h . A C ] 1 6 Ju n 20 04 MODULE STRUCTURE OF AN INJECTIVE RESOLUTION

ar X iv : m at h / 04 06 31 1 v 3 [ m at h . A C ] 2 0 Ju n 20 06 MODULE STRUCTURE OF AN INJECTIVE RESOLUTION

Let A be the ring obtained by localizing the polynomial ring κ[X, Y, Z, W ] over a field κ at the maximal ideal (X, Y, Z, W) and modulo the ideal (XW − Y Z). Let p be the ideal of A generated by X and Y. We study the module structure of a minimal injective resolution of A/p in details using local cohomology. Applications include the description of Ext i A (M, A/p), where M is a module construct...

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 / 06 06 31 2 v 1 [ m at h . A C ] 1 3 Ju n 20 06 ASYMPTOTIC BEHAVIOR OF MULTIGRADED REGULARITY

Let S be a standard N k-graded polynomial ring over a field K, let I be a multigraded homogeneous ideal of S, and let M be a finitely generated Z k-graded S-module. We prove that the resolution regularity, a multigraded variant of Castelnuovo-Mumford regularity, of I n M is asymptotically a linear function. This shows that the well known Z-graded phenomenon carries to multigraded situation.

ar X iv : a st ro - p h / 04 06 56 7 v 1 2 4 Ju n 20 04 1

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...