共查询到20条相似文献,搜索用时 15 毫秒
1.
M. I. Kabenyuk 《Ukrainian Mathematical Journal》1990,42(2):145-148
It is established that the number of compact Cartan subgroups of a connected Lie group is determined by the topological size of the set of its compact elements. This fact clarifies the structure of those connected Lie groups in which the set indicated is everywhere dense.Translated from Ukrainskii Matematicheskii Zhurnal, Vol 42, No. 2, pp. 164–168, February, 1990. 相似文献
2.
Nourredine Bounechada 《Bulletin des Sciences Mathématiques》2004,128(4):315-322
It is well known that we have an algebraic characterization of connected Lie groups of polynomial volume growth: a Lie group G has polynomial volume growth if and only if it is of type R. In this paper, we shall give a geometric characterization of connected Lie groups of polynomial volume growth in terms of the distance distortion of the subgroups. More precisely, we prove that a connected Lie group G has polynomial volume growth if and only if every closed subgroup has a polynomial distortion in G. 相似文献
3.
J. M. Mø ller D. Notbohm 《Transactions of the American Mathematical Society》1998,350(9):3483-3504
Finite loop spaces are a generalization of compact Lie groups. However, they do not enjoy all of the nice properties of compact Lie groups. For example, having a maximal torus is a quite distinguished property. Actually, an old conjecture, due to Wilkerson, says that every connected finite loop space with a maximal torus is equivalent to a compact connected Lie group. We give some more evidence for this conjecture by showing that the associated action of the Weyl group on the maximal torus always represents the Weyl group as a crystallographic group. We also develop the notion of normalizers of maximal tori for connected finite loop spaces, and prove for a large class of connected finite loop spaces that a connected finite loop space with maximal torus is equivalent to a compact connected Lie group if it has the right normalizer of the maximal torus. Actually, in the cases under consideration the information about the Weyl group is sufficient to give the answer. All this is done by first studying the analogous local problems.
4.
《代数通讯》2013,41(12):5439-5463
The explicit formula for the distortion function of a connected Lie subgroup in a connected simply connected nilpotent Lie group is obtained. In particular, we prove that a function f: N → R can be realized (up to equivalence) as the distortion function of a connected Lie subgroup in a connected simply connected nilpotent Lie group if and only if f ~ nr for some nonnegative r ∈ Q. Considering lattices in Lie groups, we establish the analogous results for finitely generated nilpotent groups. 相似文献
5.
Using a strong version of the Curve Selection Lemma for real semianalytic sets, we prove that for an arbitrary connected Lie group G, each connected component of the set E_n(G)of all elements of order n in G is a conjugacy class in G. In particular, all conjugacy classes of finite order in G are closed. Some properties of connected components of E_n(G) are also given. 相似文献
6.
LetG be a Lie group with Lie algebraL(G) and let Ω be a non-empty subset ofL(G). If Ω is interpreted as the set of controls, then the set of elements attainable from the identity for the system Ω is a
subsemigroup ofG.
A system Ω is called anon-overlapping control system if any element attainable for Ω is only attainable at one time. In this paper, we show that a compact convex generating nonoverlapping
control systems on a connected Lie group must be contained inX+E for someX∈L(G)\E, where E is a subspace of codimension one containing the commutator, and the homomorphism from the attainable semigroup intoR
+ extends continuously to the whole group in the case of solvable Lie groups.
This work is done under the support of TGRC-KOSEF. 相似文献
7.
Adeleh Abdolghafourian Mohammad A. Iranmanesh Alice C. Niemeyer 《Journal of Pure and Applied Algebra》2017,221(10):2482-2493
The Divisibility Graph of a finite group G has vertex set the set of conjugacy class sizes of non-central elements in G and two vertices are connected by an edge if one divides the other. We determine the connected components of the Divisibility Graph of the finite groups of Lie type in odd characteristic. 相似文献
8.
In this paper,the authors determine maximal connected automorphism group of the Lie transformation group T(D(VN,F)),which acting on the normal Siegel domain D(VN,F)is simple and transitive,and prove that the maximal connected automorphism group of T(D(VN,F))is its maximal connected inner automorphism group. 相似文献
9.
It is shown that for a large class of Lie groups (called weakly algebraic groups) including all connected semisimple Lie groups the following holds: for any probability measure on the Lie group the set of all two-sided convolution factors is compact if and only if the centralizer of the support of inG is compact. This is applied to prove that for any connected Lie groupG, any homomorphism of any real directed (submonogeneous) semigroup into the topological semigroup of all probability measures onG is locally tight. 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.
Karl-Hermann Neeb 《Monatshefte für Mathematik》2000,42(1):123-153
In this paper we give a characterization of those reductive or solvable connected, not necessarily simply connected, Lie groups which permit a non-degenerate group order. A non-degenerate group ordering on G always defines a pointed generating invariant convex cone W in the Lie algebra of G, but not every such cone arises in this way. The cones that do are called global. To decide whether a given cone is global or not is a difficult problem which for simply connected groups and invariant cones has completely been solved by Gichev. 相似文献
12.
We prove that the asymptotic Assouad–Nagata dimension of a connected Lie group G equipped with a left-invariant Riemannian metric coincides with its topological dimension of G/C where C is a maximal compact subgroup. To prove it we will compute the Assouad–Nagata dimension of connected solvable Lie groups and semisimple Lie groups. As a consequence we show that the asymptotic Assouad–Nagata dimension of a polycyclic group equipped with a word metric is equal to its Hirsch length and that some wreath-type finitely generated groups can not be quasi-isometrically embedded into any cocompact lattice on a connected Lie group. 相似文献
13.
Let B(R^n) be the set of all n x n real matrices, Sr the set of all matrices with rank r, 0 ≤ r ≤ n, and Sr^# the number of arcwise connected components of Sr. It is well-known that Sn =GL(R^n) is a Lie group and also a smooth hypersurface in B(R^n) with the dimension n × n. 相似文献
14.
Mathematical Notes - Let $$G$$ be a type I connected and simply connected generalized diamond Lie group defined as the semidirect product of a $$d$$ -dimensional Abelian Lie group $$N$$ with... 相似文献
15.
16.
《Mathematische Nachrichten》2017,290(14-15):2341-2355
In this paper, we use the powerful tool Milnor bases to determine all the locally symmetric left invariant Riemannian metrics up to automorphism, on 3‐dimensional connected and simply connected Lie groups, by solving system of polynomial equations of constants structure of each Lie algebra . Moreover, we show that E 0(2) is the only 3‐dimensional Lie group with locally symmetric left invariant Riemannian metrics which are not symmetric. 相似文献
17.
M. McCrudden 《Monatshefte für Mathematik》1984,98(4):295-310
The behaviour of the supports of an absolutely continuous Gauss semigroup on certain Lie groups is discussed. It is shown that on a connected nilpotent Lie group any absolutely continuous Gauss semigroup has full supports but on compact connected Lie groups which are not Abelian there exist absolutely continuous Gauss semigroups which do not have common supports. 相似文献
18.
We compute the covering dimension of the asymptotic cone ofa connected Lie group. For simply connected solvable Lie groups,this is the codimension of the exponential radical. As an application of the proof, we give a characterization ofconnected Lie groups that quasi-isometrically embed into a nonpositivelycurved metric space. Received February 6, 2007. 相似文献
19.
Karl-Hermann Neeb 《Monatshefte für Mathematik》2000,131(2):123-153
In this paper we give a characterization of those reductive or solvable connected, not necessarily simply connected, Lie
groups which permit a non-degenerate group order. A non-degenerate group ordering on G always defines a pointed generating invariant convex cone W in the Lie algebra of G, but not every such cone arises in this way. The cones that do are called global. To decide whether a given cone is global
or not is a difficult problem which for simply connected groups and invariant cones has completely been solved by Gichev.
(Received 22 October 1999; in revised form 3 March 2000) 相似文献
20.
A. A. George Michael 《Results in Mathematics》2010,58(1-2):37-38
We prove that normal subgroups of a finite dimensional real, not necessarily connected, Lie group with semisimple Lie algebra are closed. This generalizes a result of Ragozin (Proc AMS 32:632–633, 1972) who proved this for connected Lie groups; our proof is new even in this special case. 相似文献