RESTRICTED LIE ALGEBRAS WITH MAXIMAL 0-PIM

In this paper it is shown that the projective cover of the trivial irreducible module of a finite-dimensional solvable restricted Lie algebra is induced from the one dimensional trivial module of a maximal torus. As a consequence, the number of the isomorphism classes of irreducible modules with a fixed p-character for a finite-dimensional solvable restricted Lie algebra L is bounded above by p ^MT(L), where MT(L) denotes the maximal dimension of a torus in L. Finally, it is proved that in characteristic p > 3 the projective cover of the trivial irreducible L-module is induced from the one-dimensional trivial module of a torus of maximal dimension, only if L is solvable.     

Competitive H-bonding in bicyclic bis-lactams: self-assembly in nanotubes or in unbalanced chiral threefold interpenetrated diamondoid network

The first example of an H-bonded diamondoid network formed by a chiral molecule is reported. Diamondoid networks in the crystal structure of the described bicyclic bis-lactam are homochiral and threefold interpenetrated, two of them being of one chirality and the third of the other. Thus, imbalanced chiral packing with ee 33% is observed. A slight change in the structural formula leads to an entirely different crystal structure with nanosize channels.