ﻻ يوجد ملخص باللغة العربية
We interpret an open orbit in a 32-dimensional representation space of Spin(9,1) x SL(2,R) as a substitute for the non-existent group of invertible 2x2 matrices over the octonions and study various natural homogeneous subspaces. The approach is via twistor geometry in eight dimensions.
The main purpose of this paper is calculation of differential invariants which arise from prolonged actions of two Lie groups SL(2) and SL(3) on the $n$th jet space of $R^2$. It is necessary to calculate $n$th prolonged infenitesimal generators of the action.
We prove simplicity, and compute $delta$-derivations and symmetric associative forms of algebras in the title.
We show that for every nonelementary representation of a surface group into $SL(2,{mathbb C})$ there is a Riemann surface structure such that the Higgs bundle associated to the representation lies outside the discriminant locus of the Hitchin fibration.
We consider the action of $SL(2,mathbb{R})$ on a vector bundle $mathbf{H}$ preserving an ergodic probability measure $ u$ on the base $X$. Under an irreducibility assumption on this action, we prove that if $hat u$ is any lift of $ u$ to a probabilit
In this paper we develop two coadjoint orbit constructions for the phase spaces of the generalised $Sl(2)$ and $Sl(3)$ KdV hierachies. This involves the construction of two group actions in terms of Yang Baxter operators, and an Hamiltonian reduction