The theorem of Hochster and Roberts says that for any module V of a linearly reductive group G over a eld K the invariant ring KV ] G is Cohen-Macaulay. We prove the following converse: if G is a reductive group and KV ] G is Cohen-Macaulay for any module V , then G is linearly reductive.

Lusztig has given a construction of certain representations of reductive groups over finite local principal ideal rings of characteristic p, extending the construction of Deligne and Lusztig of representations of reductive groups over finite fields. We generalize Lusztig’s results to reductive groups over arbitrary finite local rings. This generalization uses the Greenberg functor and the theor...

Reductive Claisen rearrangement of 1-allyloxy-8-methoxy-9, 10-anthraquinone followed by demethylation and reduction, and of 1,8-bisallyloxy-9,lO-anthraquinone followed by reduction provides regiospecific syntheses of 2-propyl- and 2,7-dipropyl anthralin

In this paper, I construct noncompact analogs of the Chern classes of equivariant vector bundles over complex reductive groups. Then “Chern classes” of the tangent bundle are used to carry over to the case of an arbitrary reductive group some of the well-known results that hold for a complex torus. One of the results of this paper is a formula for the Chern classes of all regular equivariant co...

The first systematic mechanism study of C-F reductive elimination from a transition metal complex is described. C-F bond formation from three different Pd(IV) fluoride complexes was mechanistically evaluated. The experimental data suggest that reductive elimination occurs from cationic Pd(IV) fluoride complexes via a dissociative mechanism. The ancillary pyridyl-sulfonamide ligand plays a cruci...

A method, due tó Elie Cartan, is used to give an algebraic classification of the non-reductive homogeneous pseudo-Riemannian manifolds of dimension four. Only one case with Lorentz signature can be Einstein without having constant curvature, and two cases with (2,2) signature are Einstein of which one is Ricci-flat. If a four-dimensional non-reductive homogeneous pseudo-Riemannian manifold is s...

The first enantioselective organocatalytic reductive amination reaction has been accomplished. The development of a new chiral phosphoric acid catalyst has provided a convenient strategy for the enantioselective construction of protected primary amines and provided a highly stereoselective method for the reductive amination of heterocyclic amines. A diverse spectrum of ketone and amine substrat...

0. Introduction 1 1. Main definitions 3 2. Polarized stable reductive varieties 4 2.1. Classification 4 2.2. Cohomology groups 8 3. Pairs 9 4. Moduli of stable reductive pairs 10 4.1. General remarks on families 10 4.2. One-parameter degenerations 11 4.3. Construction of the moduli space of pairs 13 4.4. Projectivity of the moduli space 17 4.5. Structure of the moduli space 18 5. Connection wit...

A method, due tó Elie Cartan, is used to give an algebraic classification of the non-reductive homogeneous pseudo-Riemannian manifolds of dimension four. Only one case with Lorentz signature can be Einstein without having constant curvature, and two cases with (2,2) signature are Einstein of which one is Ricci-flat. If a four-dimensional non-reductive homogeneous pseudo-Riemannian manifold is s...

Monomeric, three-coordinate arylpalladium(II) halide complexes undergo reductive elimination of aryl halide to form free haloarene and Pd(0). Reductive elimination of aryl chlorides, bromides, and iodides were observed upon the addition of P(t-Bu)3 to Pd[P(t-Bu)3](Ar)(X) (X = Cl, Br, I). Conditions to observe the equilibrium between reductive elimination and oxidative addition were established ...