22,790 research outputs found
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
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