Let EG be a stable principal G–bundle over a compact connected Kähler manifold, where G is a connected reductive linear algebraic group defined over C. Let H ⊂ G be a complex reductive subgroup which is not necessarily connected, and let EH ⊂ EG be a holomorphic reduction of structure group. We prove that EH is preserved by the Einstein–Hermitian connection on EG. Using this we show that if EH ...

Desulfomonile tiedjei DCB-1, a sulfate-reducing bacterium, conserves energy for growth from reductive dehalogenation of 3-chlorobenzoate by an uncharacterized chemiosmotic process. Respiratory electron transport components were examined in D. tiedjei cells grown under conditions for reductive dehalogenation, pyruvate fermentation, and sulfate reduction. Reductive dehalogenation was inhibited by...

Recall that an algebraic group G is called (linearly) reductive if any its rational (i.e., algebraic) representation is completely reducible. The finite groups, the group GLn and the products GLn1 × . . .GLnk are reductive. Below G denotes a reductive algebraic group and X is an affine algebraic variety equipped with an (algebraic) action of G. Results explained below in this section can be fou...

A systematic exposition is given of the theory of invariant differential operators on a not necessarily reductive homogeneous space. This exposition is modelled on Helgason’s treatment of the general reductive case and the special nonreductive case of the space of horocycles. As a final application the differential operators on (not a priori reductive) isotropic pseudo-Riemannian spaces are cha...

We give characterizations of the property of being weakly reductive for finitely generated commutative semigroups. As a consequence of these characterizations we obtain an algorithm for determining from a presentation of a finitely generated commutative semigroup whether it is weakly reductive. Furthermore, we present some connections between cancellative finitely generated commutative semigrou...