共查询到20条相似文献,搜索用时 15 毫秒
1.
Recently, E.C. Lance extended the pointwise ergodic theorem to actions of the group of integers on von Neumann algebras. Our purpose is to extend other pointwise ergodic theorems to von Neumann algebra context: the Dunford-Schwartz-Zygmund pointwise ergodic theorem, the pointwise ergodic theorem for connected amenable locally compact groups, the Wiener's local ergodic theorem for
+
d
and for general Lie groups. 相似文献
2.
Brendan Foreman 《Differential Geometry and its Applications》2007,25(5):582-584
We restate and prove the main theorem of the paper “Complex contact Lie groups and generalized complex Heisenberg groups”. 相似文献
3.
《Quaestiones Mathematicae》2013,36(3):263-293
Abstract Bäcklund's theorem states that the most general contact transformation is an extended point transformation whenever both the number of independent variables and the number of dependent variables exceed one. A partial circumvention of Bäcklund's theorem is obtained by assigning each dependent variable its own distinct manifold of independent variables. This gives rise to extended symplectic product structures. sequences of extended Hamiltonians, and Lie groups of regular maps that satisfy systems of extended Hamilton-Jacobi equations provided the initial data is determined by a regular map. These ideas are applied to the study of systems of nonlinear second order partial differential equations. Lie groups of solutions are shown to be obtained by solving systems of extended Hamilton-Jacobi equations provided the initial data defines a solution. 相似文献
4.
In the spirit of an earlier result of D. Müller on the Heisenberg group we prove a restriction theorem on a certain class of two step nilpotent Lie groups. Our result extends that of Müller also in the framework of the Heisenberg group. 相似文献
5.
A version of Engel’s theorem for Malcev superalgebras is proved in the spirit of theJacobson-Engel theorem for Lie algebras. Some consequences for the structure of Malcev superalgebras with trivial Lie nucleus are derived. 相似文献
6.
V. A. Kaimanovich 《Journal of Mathematical Sciences》1989,47(2):2387-2398
The classical theory of Lyapunov characteristic exponents is reformulated in invariant geometric terms and carried over to arbitrary noncompact semisimple Lie groups with finite center. A multiplicative ergodic theorem (a generalization of a theorem of Oseledets) and the global law of large numbers are proved for semisimple Lie groups, as well as a criterion for Lyapunov regularity of linear systems of ordinary differential equations with subexponential growth of coefficients.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 164, pp. 30–46, 1987. 相似文献
7.
In the present article, the authors give some properties on subinvariant subalgebras of modular Lie superalgebras and obtain the derivation tower theorem of modular Lie superalgebras, which is analogous to the automorphism tower theorem of finite groups. Moreover, they announce and prove some results of modular complete Lie superalgebras. 相似文献
8.
We generalize the classical Paley–Wiener theorem to special types of connected, simply connected, nilpotent Lie groups: First we consider nilpotent Lie groups whose Lie algebra admits an ideal which is a polarization for a dense subset of generic linear forms on the Lie algebra. Then we consider nilpotent Lie groups such that the co-adjoint orbits of all the elements of a dense subset of the dual of the Lie algebra 𝔤* are flat (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
9.
Tin-Yau Tam 《Linear and Multilinear Algebra》1997,43(1):87-113
The relationship between the classical Schur-Horn's theorem on the diagonal elements of a Hermitian matrix with prescribed eigenvalues and Kostant's convexity theorem in the context of Lie groups. By using Kostant's convexity theorem, we work out the statements on the special orthogonal group and the symplectic group explicitly. Schur-Horn's result can be stated in terms of a set of inequalities. The counterpart in the Lie-theoretic context is related to a partial ordering, introduced by Atiyah and Bott, defined on the closed fundamental Weyl chamber. Some results of Thompson on the diagonal elements of a matrix with prescribed singular values are recovered. Thompson-Poon's theorem on the convex hull of Hermitian matrices with prescribed eigenvalues is also generalized. Then a result of Atiyah-Bott is recovered. 相似文献
10.
In (Kaniuth and Kumar in Math. Proc. Camb. Phil. Soc. 131, 487–494, 2001) Hardy’s uncertainty principle for was generalized to connected and simply connected nilpotent Lie groups. In this paper, we extend it further to connected
nilpotent Lie groups with non-compact centre. Concerning the converse, we show that Hardy’s theorem fails for a connected
nilpotent Lie group G which admits a square integrable irreducible representation and that this condition is necessary if the simply connected
covering group of G satisfies the flat orbit condition. 相似文献
11.
S. K. Ray 《Proceedings Mathematical Sciences》2001,111(3):293-318
We extend an uncertainty principle due to Cowling and Price to two step nilpotent Lie groups, which generalizes a classical
theorem of Hardy. We also prove an analogue of Heisenberg inequality on two step nilpotent Lie groups. 相似文献
12.
Tin-Yau Tam 《Linear and Multilinear Algebra》2013,61(1-3):87-113
The relationship between the classical Schur-Horn's theorem on the diagonal elements of a Hermitian matrix with prescribed eigenvalues and Kostant's convexity theorem in the context of Lie groups. By using Kostant's convexity theorem, we work out the statements on the special orthogonal group and the symplectic group explicitly. Schur-Horn's result can be stated in terms of a set of inequalities. The counterpart in the Lie-theoretic context is related to a partial ordering, introduced by Atiyah and Bott, defined on the closed fundamental Weyl chamber. Some results of Thompson on the diagonal elements of a matrix with prescribed singular values are recovered. Thompson-Poon's theorem on the convex hull of Hermitian matrices with prescribed eigenvalues is also generalized. Then a result of Atiyah-Bott is recovered. 相似文献
13.
The well-known tower theorem of groups (resp. Lie algebras) shows that the tower of automorphism groups (resp. derivation algebras) of a finite group (resp. a finite dimensional Lie algebra) with trivial center terminates after finitely many steps. We generalize these results for Lie rings, and present some necessary and sufficient conditions for Lie rings to be complete. 相似文献
14.
The well-known tower theorem of groups (resp. Lie algebras) shows that the tower of automorphism groups (resp. derivation algebras) of a finite group (resp. a finite dimensional Lie algebra) with trivial center terminates after finitely many steps. We generalize these results for Lie rings, and present some necessary and sufficient conditions for Lie rings to be complete. 相似文献
15.
In this paper cyclic one-cocycles of Heisenberg groups and some other Lie group are determined. The concept of almost Lie group of operators is introduced, and the trace formula is given by cyclicone cocyle on the Lie group. The Von Neumann theorem on Weyl commutation relation is generalized in certain case. 相似文献
16.
Gaven J. Martin 《Mathematische Annalen》2002,324(2):329-340
A uniformly quasiregular mapping, is a mapping of the m-sphere with the property that it and all its iterates have uniformly bounded distortion. Such maps are rational with respect to
some bounded measurable conformal structure and there is a Fatou-Julia type theory associated with the dynamical system obtained
by iterating these mappings. We begin by investigating the analogue of Siegel's theorem on the local conjuga cy of rotational
dynamics. We are led to consider the analytic continuation properties of solutions to the highly nonlinear first order Beltrami
systems. We reduce these problems to a central and well known conjecture in the theory of transformation groups; namely the
Hilbert-Smith conjecture, which roughly asserts that effective transformation groups of manifolds are Lie groups. Our affirmative
solution to this problem then implies unique analytic continuation and Siegel's theorem.
Received: 14 September 2000 / Revised version: 23 November 2001 / Published online: 5 September 2002
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ID="*" Research supported in part by grants from the Marsden Fund and Royal Society (NZ). 相似文献
17.
C. Neidhardt 《Transformation Groups》1999,4(4):375-404
In this survey we shall prove a convexity theorem for gradient actions of reductive Lie groups on Riemannian symmetric spaces. After studying general properties of gradient maps, this proof is established by (1) an explicit calculation on the hyperbolic plane followed by a transfer of the results to general reductive Lie groups, (2) a reduction to a problem on abelian spaces using Kostant's Convexity Theorem, (3) an application of Fenchel's Convexity Theorem. In the final section the theorem is applied to gradient actions on other homogeneous spaces and we show, that Hilgert's Convexity Theorem for moment maps can be derived from the results. 相似文献
18.
M. Hull 《Archiv der Mathematik》2011,96(2):131-134
In this paper, we consider the conjugacy growth function of a group, which counts the number of conjugacy classes which intersect
a ball of radius n centered at the identity. We prove that in the case of virtually polycyclic groups, this function is either exponential or
polynomially bounded, and is polynomially bounded exactly when the group is virtually nilpotent. The proof is fairly short,
and makes use of the fact that any polycyclic group has a subgroup of finite index which can be embedded as a lattice in a
Lie group, as well as exponential radical of Lie groups and Dirichlet’s approximation theorem. 相似文献
19.
We prove a generalized implicit function theorem for Banach spaces, without the usual assumption that the subspaces involved
being complemented. Then we apply it to the problem of parametrization of fibers of differentiable maps, the Lie subgroup
problem for Banach–Lie groups, as well as Weil’s local rigidity for homomorphisms from finitely generated groups to Banach–Lie
groups.
相似文献
20.
V. A. Kyrov 《Russian Mathematics (Iz VUZ)》2008,52(6):25-36
In the theory of physical structures the classification of metric functions (both on a single set and on two ones) plays an important role. A metric function represents a two-point invariant of a certain local Lie transformation group. Moreover, one can uniquely restore this group with the help of the invariance condition. According to this theorem, in order to find all metric functions, it suffices to construct the complete classification of local Lie transformation groups. In this paper we classify Lie algebras of simply transitive local Lie groups of local transformations of a four-dimensional space, and then we define metric functions. The obtained results admit application in physics, in particular, in thermodynamics. 相似文献