اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدDifferential Invariants of SL(2) and SL(3)-ACTIONS on R^2
145
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
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.
قيم البحث
اقرأ أيضاً
A superspace formulation of IIB supergravity which includes the field strengths of the duals of the usual physical one, three and five-form field strengths as well as the eleven-form field strength is given. The superembedding formalism is used to co
nstruct kappa-symmetric SL(2,R) covariant D-brane actions in an arbitrary supergravity background.
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.
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
of the coadjoint orbits. The Poisson brackets are reproduced by the Kirillov construction. From this construction we obtain a `natural gauge fixing proceedure for the generalised hierarchies.
Let $Gamma$ = SL 3 (Z[ 1 2 , i]), let X be any mod-2 acyclic $Gamma$-CW complex on which $Gamma$ acts with finite stabilizers and let Xs be the 2-singular locus of X. We calculate the mod-2 cohomology of the Borel constructon of Xs with respect to th
e action of $Gamma$. This cohomology coincides with the mod-2 cohomology of $Gamma$ in cohomological degrees bigger than 8 and the result is compatible with a conjecture of Quillen which predicts the strucure of the cohomology ring H * ($Gamma$; Z/2).
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
y measure on the projectivized bunde $mathbb{P}(mathbf{H})$ that is invariant under the upper triangular subgroup, then $hat u$ is supported in the projectivization $mathbb{P}(mathbf{E}_1)$ of the top Lyapunov subspace of the positive diagonal semigroup. We derive two applications. First, the Lyapunov exponents for the Kontsevich-Zorich cocycle depend continuously on affine measures, answering a question in [MMY]. Second, if $mathbb{P}(mathbf{V})$ is an irreducible, flat projective bundle over a compact hyperbolic surface $Sigma$, with hyperbolic foliation $mathcal{F}$ tangent to the flat connection, then the foliated horocycle flow on $T^1mathcal{F}$ is uniquely ergodic if the top Lyapunov exponent of the foliated geodesic flow is simple. This generalizes results in [BG] to arbitrary dimension.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
