This work describes the design and application of a single-pot, reductive arene C-H silanolization of aromatic esters for synthesis of ortho-formyl arylsilanols. This strategy involves a sequence of two transition metal (Ir and Rh)-catalyzed reactions for reductive arene ortho-silylation directed by hydridosilyl acetals and hydrolysis.

We give an efficient algorithm for Lang's Theorem in split connected reductive groups defined over finite fields of characteristic greater than 3. This algorithm can be used to construct many important structures in finite groups of Lie type. We use an algorithm for computing a Chevalley basis for a split reductive Lie algebra, which is of independent interest.

Let G be a reductive algebraic group and H its reductive subgroup. Fix a Borel subgroup B ⊂ G and a maximal torus T ⊂ B. The Cartan space aG,G/H is, by definition, the subspace of Lie(T )∗ generated by the weights of B-semiinvariant rational functions on G/H . We compute the spaces aG,G/H.

We show that near closed points with linearly reductive stabilizer, Artin stacks are formally locally quotient stacks by the stabilizer and conjecture that the statement holds étale locally. In particular, we prove that if the stabilizer of a point is linearly reductive, the stabilizer acts algebraically on a miniversal deformation space generalizing results of Pinkham and Rim.

Let G be a connected reductive linear algebraic group. The aim of this note is to settle a question of J-P. Serre concerning the behaviour of his notion of G-complete reducibility under separable field extensions. Part of our proof relies on the recently established Tits Centre Conjecture for the spherical building of the reductive group G.

An iron-catalysed, hydride-mediated reductive cross-coupling reaction has been developed for the preparation of alkanes. Using a bench-stable iron(II) pre-catalyst, reductive cross-coupling of vinyl iodides, bromides and chlorides with aryl- and alkyl Grignard reagents successfully gave the products of formal sp(3)-sp(3) cross-coupling reactions.

A reductive structure is associated here with Lagrangian canonically defined conserved quantities on gauge-natural bundles. Infinitesimal parametrized transformations defined by the gauge-natural lift of infinitesimal principal automorphisms induce a variational sequence such that the generalized Jacobi morphism is naturally self-adjoint. As a consequence, its kernel defines a reductive split s...

The study of left-invariant Einstein metrics on compact Lie groups which are naturally reductive was initiated by J. E. D’Atri and W. Ziller in 1979. In the present work we prove existence of non-naturally reductive Einstein metrics on the compact simple Lie groups SO(n) (n ≥ 11), Sp(n) (n ≥ 3), E6, E7, and E8.

We give an explicit description of a set of irreducible representations of a Weyl group which parametrizes the nilpotent orbits in the Lie algebra of a connected reductive group in arbitrary characteristic. We also answer a question of Serre concerning the conjugacy class of a power of a unipotent element in a connected reductive group.

We will prove that any weakly-split spherical Tits system (B,N) inG = G(k) (G a reductive or a pseudo-reductive k-group) satisfying some natural conditions is “standard”. In particular, if G is anisotropic over k, then such a Tits system is trivial, i.e., B = G.