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1.
We introduce the notion of a conformal de Rham complex of a Riemannian manifold. This is a graded differential Banach algebra and it is invariant under quasiconformal maps, in
particular the associated cohomology is a new quasiconformal invariant. 相似文献
2.
We study the graded Poisson structures defined on Ω(M), the graded algebra of differential forms on a smooth manifoldM, such that the exterior derivative is a Poisson derivation. We show that they are the odd Poisson structures previously studied
by Koszul, that arise from Poisson structures onM. Analogously, we characterize all the graded symplectic forms on ΩM) for which the exterior derivative is a Hamiltomian graded vector field. Finally, we determine the topological obstructions
to the possibility of obtaining all odd symplectic forms with this property as the image by the pullback of an automorphism
of Ω(M) of a graded symplectic form of degree 1 with respect to which the exterior derivative is a Hamiltonian graded vector field. 相似文献
3.
Mark V. Losik 《Annals of Global Analysis and Geometry》1995,13(4):323-338
The complex ofG-invariant forms and its cohomology for arbitraryG-manifolds and especially for a certain class ofG-manifolds, which are locally trivial fiber bundles over the orbit space, are considered. The transgression in the differential graded algebra of basic elements for tensor product of two identical Weil algebras of a reductive Lie groupG is calculated. This is used to get two convenient differential graded algebras with the same minimal models as the differential algebra of differential forms on the cross product of two principalG-bundles overG and ofG-invariant forms onG-manifolds of the above class. In particular, for compactG the generalization of the Cartan theorem on the cohomology of a homogeneous space is proved.Partially supported by the grant of the AMS's fSU Aid Fund 相似文献
4.
Using maps due to Ozeki and Broué-Enguehard between graded spaces of invariants for certain finite groups and the algebra of modular forms of even weight we equip these invariants spaces with a differential operator which gives them the structure of a Rankin-Cohen algebra. A direct interpretation of the Rankin-Cohen bracket in terms of transvectant for the group SL(2, C) is given. 相似文献
5.
V. V. Zharinov 《Theoretical and Mathematical Physics》1999,118(2):129-151
Derivations of the Heisenberg algebraH and some related questions are studied. The ideas and the language of formal differential geometry are used. It is proved
that all derivations of this algebra are inner. The main subalgebras of the Lie algebraD(H) of all derivations ofH are distinguished, and their properties are studied. It is shown that the algebraH interpreted as a Lie algebra (with the commutator as the Lie bracket) forms a one-dimensional central extension ofD(H).
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 118. No. 2 pp. 163–189, February, 1999. 相似文献
6.
Hans Tilgner 《Journal of Pure and Applied Algebra》1977,10(2):163-168
Graded skew bilinear forms {,} on graded vector spaces V are defined such that their restrictions to the even resp. odd subspaces are skew resp. odd. Over such graded symplectic vector spaces a (universal) factor algebra of the tensor algebra of V is described which reduces to a Weyl- resp. Clifford algebra if only one even resp. odd subspace is nontrivial. Introducing the total graduation on this polynomial algebra and graded symmetrization it is shown that the elements up to second power are closed under graded commutation. If the graduation is of type Z2 the elements of second power are a Lie-graded algebra and this is the only graduation for which this is true. The graded commutation relations of this algebra are calculated. It is isomorphic to the graded symplectic algebra of (V,{,}) which is contained in the graded derivation algebra of the graded Heisenberg algebra of elements up to first power. 相似文献
7.
A rather simple natural outer derivation of the graded Lie algebra of all vector valued differential forms with the Frölicher-Nijenhuis bracket turns out to be a differential and gives rise to a cohomology of the manifold, which is functorial under local diffeomorphisms. This cohomology is determined as the direct product of the de Rham cohomology space and the graded Lie algebra of traceless vector valued differential forms, equipped with a new natural differential concomitant as graded Lie bracket. We find two graded Lie algebra structures on the space of differential forms. Some consequences and related results are also discussed. 相似文献
8.
Let A be a graded algebra. It is shown that the derived category of dg modules over A (viewed as a dg algebra with trivial differential) is a triangulated hull of a certain orbit category of the derived category of graded A-modules. This is applied to study derived categories of graded gentle one-cycle algebras. 相似文献
9.
In this paper the usualZ
2 graded Lie algebra is generalized to a new form, which may be calledZ
2,2 graded Lie algebra. It is shown that there exist close connections between theZ
2,2 graded Lie algebra and parastatistics, so theZ
2,2 can be used to study and analyse various symmetries and supersymmetries of the paraparticle systems 相似文献
10.
Homogeneous graded metrics over split ℤ2-graded manifolds whose Levi-Civita connection is adapted to a given splitting, in the sense recently introduced by Koszul,
are completely described. A subclass of such is singled out by the vanishing of certain components of the graded curvature
tensor, a condition that plays a role similar to the closedness of a graded symplectic form in graded symplectic geometry:
It amounts to determining a graded metric by the data {g, ω, Δ′}, whereg is a metric tensor onM, ω 0 is a fibered nondegenerate skewsymmetric bilinear form on the
Batchelor bundleE → M, and Δ′ is a connection onE satisfying Δ′ω = 0. Odd metrics are also studied under the same criterion and they are specified by the data {κ, Δ′}, with
κ ∈ Hom (TM, E) invertible, and Δ′κ = 0. It is shown in general that even graded metrics of constant graded curvature can be supported only
over a Riemannian manifold of constant curvature, and the curvature of Δ′ onE satisfiesR
Δ′ (X,Y)2 = 0. It is shown that graded Ricci flat even metrics are supported over Ricci flat manifolds and the curvature of the connection
Δ′ satisfies a specific set of equations. 0 Finally,
graded Einstein even metrics can be supported only over Ricci flat Riemannian manifolds. Related results for graded metrics
on Ω(M) are also discussed.
Partially supported by DGICYT grants #PB94-0972, and SAB94-0311; IVEI grant 95-031; CONACyT grant #3189-E9307. 相似文献
11.
Yasushi Homma 《Transactions of the American Mathematical Society》2006,358(1):87-114
Gradients are natural first order differential operators depending on Riemannian metrics. The principal symbols of them are related to the enveloping algebra and higher Casimir elements. We give formulas in the enveloping algebra that induce not only identities for higher Casimir elements but also all Bochner-Weitzenböck formulas for gradients. As applications, we give some vanishing theorems.
12.
David Applebaum 《Journal of Theoretical Probability》1993,6(1):17-32
A class of quantum stochastic flows on*-algebras is introduced which includes both classical flows on Riemannian manifolds and flows induced by Lie group actions onC
*-algebras. Criteria are established to determine those flows which are unitarily equivalent to ones driven by classical Brownian motion. It is shown that taking complex combinations of the driving coefficients of such flows gives rise to flows which are not of Evans-Hudson type (i.e., all driving coefficients do not preserve the relevant algebra). 相似文献
13.
In this paper, we define the notion of self-dual graded weak Hopf algebra and self-dual semilattice graded weak Hopf algebra. We give characterization of finite-dimensional such algebras when they are in structually simple forms in the sense of E. L. Green and E. N. Morcos. We also give the definition of self-dual weak Hopf quiver and apply these types of quivers to classify the finite- dimensional self-dual semilattice graded weak Hopf algebras. Finally, we prove partially the conjecture given by N. Andruskiewitsch and H.-J. Schneider in the case of finite-dimensional pointed semilattice graded weak Hopf algebra H when grH is self-dual. 相似文献
14.
Frank B. Estabrook 《Acta Appl Math》1987,8(3):293-319
This is an essay on the general concept of covariance, and its connection with the structure of the nested set of higher frame bundles over a differentiable manifold. Examples of covariant geometric objects include not only linear tensor fields, densities and forms, but affinity fields, sectors and sector forms, higher order frame fields, etc., often having nonlinear transformation rules and Lie derivatives. The intrinsic, or invariant, sets of forms that arise on frame bundles satisfy the graded Cartan-Maurer structure equations of an infinite lie algebra. Reduction of these gives invariant structure equations for Lie pseudogroups, and forG-structures of various orders. Some new results are introduced for prolongation of structure equations, and for treatment of Riemannian geometry with higher-order moving frames. The use of invariant form equations for nonlinear field physics is implicitly advocated.Research sponsored by the U.S. Army Research Office through an agreement with the National Aeronautics and Space Administration. 相似文献
15.
Viktor Abramov 《Advances in Applied Clifford Algebras》2007,17(4):577-588
We construct a q-analog of exterior calculus with a differential d satisfying d
N
= 0, where N ≥ 2 and q is a primitive Nth root of unity, on a noncommutative space and introduce a notion of a q-differential k-form. A noncommutative space we consider is a reduced quantum plane. Our construction of a q-analog of exterior calculus is based on a generalized Clifford algebra with four generators and on a graded q-differential algebra. We study the structure of the algebra of q-differential forms on a reduced quantum plane and show that the first order calculus induced by the differential d is a coordinate calculus. The explicit formulae for partial derivatives of this first order calculus are found. 相似文献
16.
Diego Conti 《Mathematische Zeitschrift》2011,268(3-4):725-751
We introduce a class of special geometries associated to the choice of a differential graded algebra contained in ${\Lambda^*\mathbb{R}^n}$ . We generalize some known embedding results, that effectively characterize the real analytic Riemannian manifolds that can be realized as submanifolds of a Riemannian manifold with special holonomy, to this more general context. In particular, we consider the case of hypersurfaces inside nearly-K?hler and ??-Einstein?CSasaki manifolds, proving that the corresponding evolution equations always admit a solution in the real analytic case. 相似文献
17.
Hardy Spaces of Differential Forms on Riemannian Manifolds 总被引:1,自引:0,他引:1
Let M be a complete connected Riemannian manifold. Assuming that the Riemannian measure is doubling, we define Hardy spaces H
p
of differential forms on M and give various characterizations of them, including an atomic decomposition. As a consequence, we derive the H
p
-boundedness for Riesz transforms on M, generalizing previously known results. Further applications, in particular to H
∞ functional calculus and Hodge decomposition, are given.
相似文献
18.
One-to-one correspondences are established between the set ofall nondegenerate graded Jacobi operators of degree -1 defined onthe graded algebra
of differential forms on a smooth, oriented,Riemannian manifold M, the space of bundle isomorphisms
, and the space of nondegenerate derivations of degree 1 havingnull square. Derivations with this property, andJacobi structures of odd
-degree are also studied throughthe action of the automorphism group of
. 相似文献
19.
Annals of Global Analysis and Geometry - For an orbifold, there are two naturally associated differential graded algebras, one is the de Rham algebra of orbifold differential forms and the other... 相似文献
20.
Let
be a (central) arrangement of hyperplanes in
and
the dependence matroid of the linear forms
. The Orlik–Solomon algebra
of a matroid
is the exterior algebra on the points modulo the ideal generated by circuit boundaries. The graded algebra
is isomorphic to the cohomology algebra of the manifold
. The Tutte polynomial
is a powerful invariant of the matroid
. When
is a rank 3 matroid and the θHi are complexifications of real linear forms, we will prove that
determines
. This result partially solves a conjecture of Falk. 相似文献