Volume 98, Issue 2-3
December 1988, pages 101-220
pp 101-108 December 1988
We prove here an analogue of Ambrose-Kakutani representation theorem for measurable flows. No measure is required and no points are dropped. This helps us to generalize a theorem due to Shelah and Weiss and answer a question due to A Ramsay.
pp 109-116 December 1988
LetR[X, Y] be a polynomial ring in two variables over a commutative ringR and letF∈R[X, Y] such thatR[X, Y]/(F)=R[Z] (a polynomial ring in one variable). In this set-up we prove thatR[X, Y]=R[F, G] for someG∈R[X, Y] if eitherR contains a field of characteristic zero orR is a seminormal domain of characteristic zero.
pp 117-152 December 1988
The paper presents a classification of all homogeneous (integrable) complex structures on compact, connected lie groups of even dimension. Thereafter, using lie algebraic methods it proves theorems about the Dolbeault cohomology rings of these complex manifolds in the semisimple case and exhibits the dramatic variation of ring structure of the Dolbeault rings of groups of rank 2. Using some specific computations forSO(9), it gives a counter-example to a long-standing conjecture about the Hodge-deRham (Frohlicher) spectral sequence.
pp 153-177 December 1988
A brief review is given of the linear fractional subgroups of the Mathieu groups. The main part of the paper then deals with the projective interpretation of the Golay codes; these codes are shown to describe Coxeter’s configuration inPG(5,3) and Todd’s configuration inPG(11,2) when interpreted projectively. We obtain two twelve-dimensional representations ofM24. One is obtained as the collineation group that permutes the twelve special points inPG(11,2); the other arises by interpreting geometrically the automorphism group of the binary Golay code. Both representations are reducible to eleven-dimensional representations ofM24.
pp 179-186 December 1988
This paper deals with some of the matching and non-matching properties of two minimal geodesics from a cut point, which is not a focal point, to the points of the submanifold. Closest cut point to the submanifold has been obtained under some additional assumptions.
pp 187-214 December 1988
Given a finite quiver without oriented cycles, we describe a family of algebras whose module category has the same derived category as that of the quiver algebra. This is done in the more general setting oft-structures in triangulated categories. A completeness result is shown for Dynkin quivers, thus reproving a result of Happel [H].
pp 215-220 December 1988
In this expository article we describe some recent results on the existence and general properties of complex homology 2-cells and contractible surfaces. The motivation for these can be directly traced back to C P Ramanujam’s important paper, ‘A topological characterization of the affine plane as an algebraic variety’. We also discuss the related results of M Miyanishi, T Sugie and T Fujita.