Gorensteinness of invariant subrings of quantum algebras

We prove Auslander-Gorenstein and \GKdim-Macaulay properties for certain invariant subrings of some quantum algebras, the Weyl algebras, and the universal enveloping algebras of finite dimensional Lie algebras.Comment: AMSTEX, 18 pages. Revised and corrected versio

Rings with Auslander Dualizing Complexes

A ring with an Auslander dualizing complex is a generalization of an Auslander-Gorenstein ring. We show that many results which hold for Auslander-Gorenstein rings also hold in the more general setting. On the other hand we give criteria for existence of Auslander dualizing complexes which show these occur quite frequently. The most powerful tool we use is the Local Duality Theorem for connected graded algebras over a field. Filtrations allow the transfer of results to non-graded algebras. We also prove some results of a categorical nature, most notably the functoriality of rigid dualizing complexes.Comment: 39 pages, AMSLaTex. Final version, to appear in J. Algebra. Corrected mistake in proof of Thm. 1.13. minor correction

Dualizing Complexes and Tilting Complexes over Simple Rings

We prove that two-sided tilting complexes, and dualizing complexes, over simple Goldie rings (with some technical conditions) are always shifts of invertible bimodules. This allows us to describe the derived Picard groups of such rings, and to deduce these are Gorenstein (and sometimes even Auslander-Gorenstein Cohen-Macaulay) rings.Comment: 9 pages, no figure