Lifting differential operators from orbit spaces
نویسندگان
چکیده
منابع مشابه
Orbit Spaces Arising from Isometric Actions on Hyperbolic Spaces
Let be a differentiable action of a Lie group on a differentiable manifold and consider the orbit space with the quotient topology. Dimension of is called the cohomogeneity of the action of on . If is a differentiable manifold of cohomogeneity one under the action of a compact and connected Lie group, then the orbit space is homeomorphic to one of the spaces , , or . In this paper we suppo...
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Cohomology of the Lie Algebras of Differential Operators: Lifting Formulas
(i) Tr(DiA) = 0 for any A ∈ A and any Di ∈ D (ii) [Di,Dj ] = ad(Qij) — inner derivation (Qij ∈ A) for any Di,Dj ∈ D (iii) Alt i,j,k Dk(Qij) = 0 for all i, j, k. The main example of such a situation is the Lie algebra ΨDifn(S 1) of the formal pseudodifferential operators on (S1)n (see [A]). The trace Tr in this example is the “noncommutative residue”, Tr(D) = the coefficient of the term x 1 · x ...
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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...
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Mathematicians routinely lift operators to structures. For instance, almost every textbook on calculus lifts addition pointwise to functions: ( f + g)(x) = f (x)+ g(x). In this particular example, the lifted operator inherits the properties of the base-level operator. Does this hold in general? In order to approach this problem, one has to make the concept of lifting precise. I argue that lifti...
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ژورنال
عنوان ژورنال: Annales scientifiques de l'École normale supérieure
سال: 1995
ISSN: 0012-9593,1873-2151
DOI: 10.24033/asens.1714