共查询到20条相似文献,搜索用时 93 毫秒
1.
Dorothee Schueth 《Geometriae Dedicata》2004,105(1):77-83
A nonflat Einstein solvmanifold (
, g) is said to be of standard type if in the associated metric Lie algebra
, the orthogonal complement
of the derived algebra is Abelian. It is an open question whether the standard condition is automatically satisfied for all
nonflat Einstein solvmanifolds. We derive certain properties of the metric Lie algebra
of a nonflat Einstein solvmanifold (
, g) under the assumption
. In particular, we obtain some new sufficient conditions which imply standard type. 相似文献
2.
We consider the moduli space
r
of polygons with fixed side lengths in five-dimensional Euclidean space. We analyze the local structure of its singularities
and exhibit a real-analytic equivalence between
r
and a weighted quotient of n-fold products of the quaternionic projective line
1 by the diagonal PSL(2,
)-action. We explore the relation between
r
and the fixed point set of an anti-symplectic involution on a GIT quotient Grℂ(2, 4)
n
/SL(4, ℂ). We generalize the Gel'fand—MacPherson correspondence to more general complex Grassmannians and to the quaternionic
context, and realize our space
r
as a quotient of a subspace in the quaternionic Grassmannian Grℍ(2, n) by the action of the group Sp(1)
n
. We also give analogues of the Gel'fand—Tsetlin coordinates on the space of quaternionic Hermitean marices and briefly describe
generalized action—angle coordinates on
r
. 相似文献
3.
G. A. Margulis 《Geometriae Dedicata》1991,37(1):1-7
Let G be a connected Lie group, let Γ be a lattice in G, and let
be a unipotent subgroup of G. It is proved that, for the natural action of
on G/Γ, every minimal closed
-invariant subset is compact.
Dedicated to Professor Jacques Tits on the occasion of his sixtieth birthday 相似文献
4.
The 3-local geometry
of the sporadic simple group Co1 has been known to have a cover
with a flag-transitive automorphism group which is a nonsplit extension of an elementary Abelian 2-group of rank 24 (the Leech lattice modulo 2) by Co1. It was conjectured that
was simply connected. We disprove this conjecture by constructing a double cover
of
. The automorphism group of
is of the shape
. However, it is not isomorphic to the involution centralizer of the Monster sporadic simple group. 相似文献
5.
We prove that if a group G is residually
, then for every
-subgroup of the group G, the set of -roots from this subgroup is a -separable
-subgroup. 相似文献
6.
For a discrete group G, we prove that a G-map between proper G–CW-complexes induces an isomorphism in G-equivariant K-homology if it induces an isomorphism in C-equivariant K-homology for every finite cyclic subgroup C of G. As an application, we show that the source of the Baum–Connes assembly map, namely K
*
G
(E(G,
in)), is isomorphic to K
*
G
(E(G,
)), where E(G,
) denotes the classifying space for the family of finite cyclic subgroups of G. Letting
be the family of virtually cyclic subgroups of G, we also establish that and related results. 相似文献
7.
A family
of convex sets is said to be in convex position, if none of its members is contained in the convex hull of the others. It is proved that there is a function N(n) with the following property. If
is a family of at least N(n) plane convex sets with nonempty interiors, such that any two members of
have at most two boundary points in common and any three are in convex position, then
has n members in convex position. This result generalizes a theorem of T. Bisztriczky and G. Fejes Tóth. The statement does not remain true, if two members of
may share four boundary points. This follows from the fact that there exist infinitely many straight-line segments such that any three are in convex position, but no four are. However, there is a function M(n) such that every family of at least M(n) segments, any four of which are in convex position, has n members in convex position. 相似文献
8.
A bijective mapping
defined on a finite group G is complete if the mapping defined by
,
, is bijective. In 1955 M. Hall and L. J. Paige conjectured that a finite group G has a complete mapping if and only if a Sylow 2-subgroup of G is non-cyclic or trivial. This conjecture is still open. In this paper we construct a complete mapping for the projective groups PSL
and PGL(2,q),q odd. As a consequence, we prove that in odd characteristic the projective groups PGL(n,q GL
, admit a complete mapping. 相似文献
9.
We prove in this paper that the Hilbert geometry associated with a bounded open convex domain
in R
n
whose boundary
is a
2 hypersuface with nonvanishing Gaussian curvature is bi-Lipschitz equivalent to the n-dimensional hyperbolic space H
n
. Moreover, we show that the balls in such a Hilbert geometry have the same volume growth entropy as those in H
n
. 相似文献
10.
ALAIN HÉNAUT 《Geometriae Dedicata》1997,65(1):89-101
A d-web in (
,0) is given by d complex analytic foliations of codimension one in (
,0) which are in general position. A d-web
in (
,0) is linear if all the leaves are (pieces of) hyperplanes in
and
is algebraic if it is associated, by duality, to a nondegenerate algebraic curve in
of degree d. We characterize linear webs in (
,0). We give explicit conditions under which a linear d-web in (
,0) is algebraic and we obtain equations for
in this case. Some related problems are discussed and some questions are posed. 相似文献
11.
Lluis Puig 《Geometriae Dedicata》1991,37(1):9-43
Let b be a block of a finite group G with an abelian defect group P and an inertial quotient E. Let us denote by L the semi-direct product of P and E. If E is cyclic and acts freely on P−{1}, we prove that the stable categories of
Gb- and
L-modules are equivalent, as a consequence of a more general result, without any hypothesis on E, about partial covering exomorphisms relating
Gb with a suitable twisted group algebra
*
à Jacques Tits à l'aube de sa sexagénie 相似文献
à Jacques Tits à l'aube de sa sexagénie 相似文献
12.
José M. Isidro 《Central European Journal of Mathematics》2007,5(3):512-522
Let G be the Banach-Lie group of all holomorphic automorphisms of the open unit ball
in a J*-algebra
of operators. Let
be the family of all collectively compact subsets W contained in
. We show that the subgroup F ⊂ G of all those g ∈ G that preserve the family
is a closed Lie subgroup of G and characterize its Banach-Lie algebra. We make a detailed study of F when
is a Cartan factor.
相似文献
13.
Christos A. Athanasiadis 《Geometriae Dedicata》2001,86(1-3):37-57
The cyclic zonotope
(n, d) is the zonotope in
d
generated by any n distinct vectors of the form (1, t, t
2,..., t
d–1). It is proved that the refinement poset of all proper zonotopal subdivisions of
(n, d) which are induced by the canonical projection :
(n, d)
(n, d), in the sense of Billera and Sturmfels, is homotopy equivalent to a sphere and that any zonotopal subdivision of
(n, d) is shellable. The first statement gives an affirmative answer to the generalized Baues problem in a new special case and refines a theorem of Sturmfels and Ziegler on the extension space of an alternating oriented matroid. An important ingredient in the proofs is the fact that all zonotopal subdivisions of
(n, d) are stackable in a suitable direction. It is shown that, in general, a zonotopal subdivision is stackable in a given direction if and only if a certain associated oriented matroid program is Euclidean, in the sense of Edmonds and Mandel. 相似文献
14.
A subsemigroup S of a semigroup Q is a straight left order in Q and Q is a semigroup of straight left quotients of S if every q ∈ Q can be written as
for some
with a
b in Q and if, in addition, every element of S that is square cancellable lies in a subgroup of Q. Here a
♯ denotes the group inverse of a in some (hence any) subgroup of Q. If S is a straight left order in Q, then Q is necessarily regular; the idea is that Q has a better understood structure than that of S. Necessary and sufficient conditions exist on a semigroup S for S to be a straight left order. The technique is to consider a pair
of preorders on S. If such a pair satisfies conditions mimicking those satisfied by
on a regular semigroup, and if certain subsemigroups of S are right reversible, then S is a straight left order. The conditions required for
to satisfy are somewhat lengthy. In this paper we aim to circumvent some of these by specialising in two ways. First we consider
only fully stratified left orders, that is, the case where
(certainly the most natural choice for
) and the other is to insist that S be abundant, that is, every
-class and every
-class of S contains an idempotent.
Our results may be used to show that the monoid of endomorphisms of a hereditary basis algebra of finite rank is a fully stratified
straight left order.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
15.
Natalie M. Priebe 《Geometriae Dedicata》2000,79(3):239-265
In this paper, a technique for analyzing levels of hierarchy in a tiling
of Euclidean space is presented. Fixing a central configuration P of tiles in
, a `derived Voronoï' tessellation
P is constructed based on the locations of copies of P in
. A family of derived Voronoï tilings
is formed by allowing the central configurations to vary through an infinite number of possibilities. The family
will normally be an infinite one, but we show that for a self-similar tiling
it is finite up to similarity. In addition, we show that if the family
is finite up to similarity, then
is pseudo-self-similar. The relationship between self-similarity and pseudo-self-similarity is not well understood, and this is the obstruction to a complete characterization of self-similarity via our method. A discussion and conjecture on the connection between the two forms of hierarchy for tilings is provided. 相似文献
16.
Given a unital C*-algebra
and a right C*-module
over
, we consider the problem of finding short smooth curves in the sphere
= {x ∈
: 〈x, x〉 = 1}. Curves in
are measured considering the Finsler metric which consists of the norm of
at each tangent space of
. The initial value problem is solved, for the case when
is a von Neumann algebra and
is selfdual: for any element x
0 ∈
and any tangent vector ν at x
0, there exists a curve γ(t) = e
tZ
(x
0), Z ∈
, Z* = −Z and ∥Z∥ ≤ π, such that γ(0) = x
0 and
(0) = ν, which is minimizing along its path for t ∈ [0, 1]. The existence of such Z is linked to the extension problem of selfadjoint operators. Such minimal curves need not be unique. Also we consider the
boundary value problem: given x
0, x
1 ∈
, find a curve of minimal length which joins them. We give several partial answers to this question. For instance, let us
denote by f
0 the selfadjoint projection I − x
0 ⊗ x
0, if the algebra f
0
f
0 is finite dimensional, then there exists a curve γ joining x
0 and x
1, which is minimizing along its path.
相似文献
17.
Necdet Güner 《Geometriae Dedicata》1996,63(1):17-23
Let N=G/ be a compact nilmanifold, G a connected, simply connected, nilpotent Lie group with its discrete subgroup and Lie algebra
. Let I* (
) denote the invariant differential forms on
.If I* (
) H* (
) is an injective map, then G is abelian and N is a torus. Furthermore, N has a formal minimal model. If N is an even-dimensional compact nilmanifold, it has a Kähler structure and invariant symplectic structure if and only if I* (
) H* (
) is injective. 相似文献
18.
Alain Rivière 《Geometriae Dedicata》2001,85(1-3):217-235
For a separable Hilbert space E whose dimension is 2 and for an open subset of E, not empty and different from E, let
be the set of all points of which have at least two projections on the close set E\, and let
be the set of all the centres of the open balls contained in and which are maximal for inclusion. We show that the Hausdorff dimension dimH(
) of
may be any real value s such that 0sdim E; we also show that can be chosen so that
is everywhere dense in and so that we have dimH(
)=1.Associons à un ouvert d'un espace de Hilbert séparable E de dimension 2, non vide et distinct de E, l'ensemble
des points de admettant plusieurs projections sur le fermé E\, et l'ensemble
des centres des boules ouvertes inclues dans et maximales pour l'inclusion. Nous montrons d'une part que la dimension de Hausdorff dimH(
) de
peut prendre toute valeur réelle s telle que 0sdim E, et d'autre part qu'on peut choisir de sorte que
soit dense dans et qu'on ait dimH(
)=1. 相似文献
19.
U. Dempwolff 《Designs, Codes and Cryptography》2001,22(2):191-207
We determine the symmetric designs
which admit a group
such that G has a nonabelian socle and is a primitiverank 3 group on points (and blocks). 相似文献
20.
Zvonko Čerin 《Geometriae Dedicata》2001,84(1-3):41-47
This paper improves an old theorem about a rectangular hyperbola
: its centre lies on the pedal circle of any point on
with respect to any triangle inscribed in
. We also prove that an analogous result holds for Cevian circles. These results are used to obtain new characterisations of the Feuerbach, Jarabek, and Kiepert hyperbolas of a triangle. 相似文献