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 nongraded algebras.
We also prove some results of a categorical nature, most notably the functoriality of rigid dualizing complexes. The space of those linear forms on the space of pi which are invariant under an orthogonal group is computed. For the corresponding group of orthogonal similitudes, it is shown that the dimension of the space of invariant linear forms is always at most one. Using positivity properties of the canonical basis it is shown that B-greater than or equal to 0 has an algebraic cell decomposition indexed by pairs of elements w less than or equal to w' of the Weyl group. I of the generic module induced from p.