Reductive megalomania

Reductive Groups

Quasi-reductive (bi)parabolic subalgebras in reductive Lie algebras

We say that a finite dimensional Lie algebra is quasi-reductive if it has a linear form whose stabilizer for the coadjoint representation, modulo the center, is a reductive Lie algebra with a center consisting of semisimple elements. Parabolic subalgebras of a semisimple Lie algebra are not always quasi-reductive (except in types A or C by work of Panyushev). The classification of quasireductiv...

Essentially Reductive Hilbert Modules

Consider a Hilbert space obtained as the completion of the polynomials C[z ] in m-variables for which the monomials are orthogonal. If the commuting weighted shifts defined by the coordinate functions are essentially normal, then the same is true for their restrictions to invariant subspaces spanned by monomials. This generalizes the result of Arveson [4] in which the Hilbert space is the m-shi...

DNA-catalyzed reductive amination.

Deoxyribozymes are particular DNA sequences that have catalytic ability, analogous to protein enzymes as functional amino acid sequences. The discovery of natural RNA enzymes (ribozymes) spurred the search for artificial deoxyribozymes, which are identified by in vitro selection. Most deoxyribozyme-catalyzed reactions involve phosphodiester bond cleavage or ligation, although other reactions su...

Enantioselective organocatalytic reductive amination.

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...