共查询到20条相似文献,搜索用时 15 毫秒
1.
Xusheng LIU 《数学年刊B辑(英文版)》2008,29(3):317-332
In this paper, the partial positivity (resp., negativity) of the curvature of all irreducible Riemannian symmetric spaces is determined. From the classifications of abstract root systems and maximal subsystems, the author gives the calculations for symmetric spaces both in classical types and in exceptional types. 相似文献
2.
Symmetric spaces or more general symmetric k-varieties can be defined as the homogeneous spaces G
k
/K
k
, where G is a reductive algebraic group defined over a field k of characteristic not 2, K the fixed point group of an involution θ of G and G
k
resp. K
k
the sets k-rational points of G resp. K. These symmetric spaces have a fine structure of root systems, characters, Weyl groups etc., similar to the underlying algebraic
group G. The relationship between the fine structure of the symmetric space and the group plays an important role in the study of
these symmetric spaces and their applications. To develop a computer algebra package for symmetric spaces one needs explicit
formulas expressing the fine structure of the symmetric space and group in terms of each other. In this paper we consider
the case that k is algebraically closed and give explicit algorithmic formulas for expressing the characters of the weight lattice
of the symmetric space in terms of the characters of the weight lattice
of the group. These algorithms can easily be implemented in a computer algebra package.
The root system of the symmetric space
can be described as the image of the root system of the group
under a projection π derived from an involution θ on
. This implies that
. Using these formulas for the characters of each of these lattices we show that in fact
.
A.G. Helminck is partially supported by N.S.F. Grant DMS-0532140. 相似文献
3.
在本文中,我们利用李群及其表示理论作为主要工具, 讨论了紧黎曼对称空间到Grassmann 流形的等变等距极小浸入问题. 相似文献
4.
Jennifer R. Daniel 《代数通讯》2013,41(5):1758-1788
In the last two decades much of the algebraic/combinatorial structure of Lie groups, Lie algebras, and their representations has been implemented in several excellent computer algebra packages, including LiE, GAP4, Chevie, Magma, and Maple. The structure of reductive symmetric spaces or more generally symmetric k-varieties is very similar to that of the underlying Lie group, with a few additional complications. A computer algebra package enabling one to do computations related to these symmetric spaces would be an important tool for researchers in many areas of mathematics, including representation theory, Harish Chandra modules, singularity theory, differential and algebraic geometry, mathematical physics, character sheaves, Lie theory, etc. In this article we lay the groundwork for computing the fine structure of symmetric spaces over the real numbers and other base fields, give a complete set of algorithms for computing the fine structure of symmetric varieties and use this to compute nice bases for the local symmetric varieties. 相似文献
5.
The real characteristic Pontryagin classes of generalized symmetric spaces with simple compact principal Lie groups are calculated in this paper. 相似文献
6.
The authors derive a formula for the volume of a compact domain in a symmetric space from normal sections through a special submanifold in the symmetric space.This formula generalizes the volume of classical domains as tubes or domains given as motions along the submanifold.Finally,some stereological considerations regarding this formula are provided. 相似文献
7.
8.
无限维项链李代数是新的一类无限维李代数,本文重点讨论了由特殊箭图诱导的项链李子代数,并证明了其中一些李子代数是半单李代数. 相似文献
9.
MARTIN LANZENDORF 《Geometriae Dedicata》1997,66(2):187-202
The purpose of this article is to study some simply connected Lie groups with left invariant Einstein metric, negative Einstein constant and nonpositive sectional curvature. These Lie groups are classified if their associated metric Lie algebra s is of Iwasawa type and s = An1n2...nr, where all niare Lie algebras of Heisenberg type with [[ni,nj] = {0} for ij. The most important ideas of the article are based on a construction method for Einstein spaces introduced by Wolter in 1991. By this method some new examples of Einstein spaces with nonpositive curvature are constructed. In another part of the article it is shown that Damek-Ricci spaces have negative sectional curvature if and only if they are symmetric spaces. 相似文献
10.
11.
本文首先证明了从复流形到对称空间的多重调和映射空间与扩张提升空间之间在相差一规范变换下存在一一对应,并给出确定的环路群在扩张提升空间的作用,因而也给出多重调和映射空间上的作用.其次,利用环路群及其代数的Iwasawa分解给出从Cn到对称空间的有限型的多重调和映射不同于文[1]中的刻划. 相似文献
12.
L. G. Rybnikov 《Functional Analysis and Its Applications》2003,37(2):114-122
A Riemannian homogeneous space X=G/H is said to be commutative if the algebra of G-invariant differential operators on X is commutative and weakly commutative if the associated Poisson algebra is commutative. Clearly, the commutativity of X implies its weak commutativity. The converse implication is proved in this paper. 相似文献
13.
14.
引进了第III类典型域上的内切超圆坐标;计算出了矩阵极坐标下相应于不变度量的体积元素;利用积分变换构造出了不变度量的Laplace-Beltrami算子的热核. 相似文献
15.
Qi DING 《数学年刊B辑(英文版)》2011,32(1):27-44
In this paper, the motion of inverse mean curvature flow which starts from a closed star-sharped hypersurface in special rotationally
symmetric spaces is studied. It is proved that the flow converges to a unique geodesic sphere, i.e., every principle curvature
of the hypersurfaces converges to a same constant under the flow. 相似文献
16.
In this paper, we study biharmonic hypersurfaces in Einstein manifolds. Then, we determine all the biharmonic hypersurfaces in irreducible symmetric spaces of compact type which are regular orbits of commutative Hermann actions of cohomogeneity one. 相似文献
17.
姚裕丰 《数学年刊A辑(中文版)》2012,33(4):483-496
设L=H(2r;1)或K(2r+1;1)是定义在特征p>2的代数封闭域F上的限制Hamiltonian型或Contact型李代数.在对广义Jacobson-Witt代数及特殊代数不可约表示的研究基础上,通过定义L的如下阶化:L=L[q],I,其中I是{1,2,…,r}的子集,得到当p-特征函数χ是正则半单时,所有不可约Uχ(L)-模都是从不可约Uχ(L[O].I)-模诱导的. 相似文献
18.
Xian Zhang 《Linear and Multilinear Algebra》2004,52(5):349-358
Suppose F is a field of characteristic not 2. Let MnF and SnF be the n × n full matrix space and symmetric matrix space over F, respectively. All additive maps from SnF to SnF (respectively, MnF) preserving Moore-Penrose inverses of matrices are characterized. We first characterize all additive Moore-Penrose inverse preserving maps from SnF to MnF, and thereby, all additive Moore-Penrose inverse preserving maps from SnF to itself are characterized by restricting the range of these additive maps into the symmetric matrix space. 相似文献
19.
We define symmetric spaces in arbitrary dimension and over arbitrary non-discrete topological fields
, and we construct manifolds and symmetric spaces associated to topological continuous quasi-inverse Jordan pairs and -triple systems. This class of spaces, called smooth generalized projective geometries, generalizes the well-known (finite or infinite-dimensional) bounded symmetric domains as well as their ‘compact-like’ duals. An interpretation of such geometries as models of Quantum Mechanics is proposed, and particular attention is paid to geometries that might be considered as ‘standard models’ – they are associated to associative continuous inverse algebras and to Jordan algebras of hermitian elements in such an algebra.Mathematics Subject Classiffications (2000). primary: 17C36, 46H70, 17C65; secondary:
17C30, 17C90 相似文献
20.
In this paper, we use Block’s results to classify irreducible modules over the diamond Lie algebra 𝔇. As a corollary, we also give a classification of irreducible modules over the Euclidean algebra 𝔢(2). 相似文献