李群的解析对合自同构对的分类

本文给出复单李代数的对合自同构对的分类,并利用它研究单连通,单李群的解析对合自同构对的分类.     

Laurent多项式代数C[x_1~(±1),x_2~(±1)]上的李三系

设A为交换变元x_1,x_2的罗朗多项式代数,记A的导子代数Der A为M.本文确定了A,M的对合自同构.利用M的对合自同构给出了一类无限维单李三系,并且通过讨论M的自同构与对合自同构的关系,确定这些单李三系的自同构.     

充当自同构群的有限群的几点注记

设p为奇素数,本文给出了中心循环中心商的阶小于p^5的有限p-群的完全分类并且给出它们中无对合自同构的群的自同构群的阶。由此,我们找到了能作为有限群自同构群的p^mq^n阶群和p^n阶群,统一和推广了Curran在1988年和Caranti与Scoppola在1990年的文章的所有结果。     

实单纯Lie代数的分类

引言实单纯Lie代数的分类,早经E.cartan解决,他是对各类复单纯Lie代数通过实际计算得到的。方法非常烦复,不足以阐明实单纯Lie代数的特征。其后E.cartan结合对称Riemann空间的研究,得出了用紧致Lie代数对合自同构的分类法的极为重要的结果。Lardy和具体地作出了这种分类;特别是后者找出了自同构的标准形。作者曾经利用的标准形作了较深入的研究,得到了所谓半单实Lie代数的“角图”,并证明了合同的角图对应的Lie代数是同构的。因此,直接从角图的结构来分类Lie代数是可能的,这便是本文所要讨论的问题,他的特点是不依赖于对合自同构的标准形及其分类方法。因之不但是直接的同时还是简单的。有趣的是这和利用所谓     

Heisenberg李(超)代数的自同构群

本文研究了Heisenberg李(超)代数的自同构群.利用Heisenberg李(超)代数与线性李(超)代数之间的同构,获得了Heisenberg李(超)代数的自同构群的子群,包括内自同构群、中心自同构群、对合自同构群.     

关于李三系的分类

首先基于复单李代数的所有对合自同构的分类,研究了复单李三系的分类.然后研究了实单李三系的分类,得到了实单李二三系或者同构于一个复单李三系的实形式,或者同构于复单李三系的实化的结论.同时还给出了关于实李三系复化和复李三系实化的部分结果.     

关于单李超三系的分类(英文)

本文证明了特征零代数闭域上的单李超三系可分为两部分:一是将单李超代数视为李超三系;二是单李超代数的对合自同构的(-1)-特征子空间.这些推广了Lister和Meyberg给出的关于单李三系分类的相应结果.     

关于逆紧全纯映射刚性的一个注记

本文对某类广义Hartogs三角形上的逆紧全纯自映射证明了刚性定理,即逆紧全纯自映射必定为全纯自同构．同时完全刻画了其全纯自同构群,并且给出了关于其全纯自同构以及两个这类域之间逆紧全纯映射的分类。     

关于逆紧全纯映射刚性的一个注记

本文对某类广义Hartogs三角形上的逆紧全纯自映射证明了刚性定理,即逆紧全纯自映射必定为全纯自同构.同时完全刻画了其全纯自同构群,并且给出了关于其全纯自同构以及两个这类域之间逆紧全纯映射的分类.     

关于特殊的实单Lie代数D4的内共轭分类

在[2]中,我们讨论了实单Lie代数的内共轭分类问题,但对于稍为困难的特殊实单Lie代数D作为例外,没有讨论.在[3]中,我们提到了可以利用定理2[3]直接证明内共轭的分类定理,但因为篇幅关系,没有给予详细的证明.在本文中,我们将讨论D_4的内共轭分类问题,并详细证明关于Satake图解的内共轭分类定理. 设of是实单Lie代数,g~c是f的复化,Autg~c,Intg~c,分别是g~c的自同构群和内自同构群;Aut(g),Int(g)Int(g)分别是g~c的自同构群拟内自同构群和内自同构群,其他符号参看[1].     

ON THE PRIMARY DECOMPOSITION THEOREM OF MODULAR LIE SUPERALGEBRAS

This gives some identities of associative Lie superalgebras and some properties of modular Lie superalgebras. Furthermore, the primary decomposition theorem of modular Lie superalgebras is shown. It is well known that the primary decomposition theorem of modular Lie algebras has played an important role in the classification of the finite-dimensional simple modular Lie algebras (see [5, 6]). Analogously, the primary decomposition theorem of modular Lie superalgebras may play an important role in the open classification of the finite dimensional simple modular Lie superalgebras.     

Positive definite Minkowski Lie algebras and bi-invariant Finsler metrics on Lie groups

In this paper, we introduce the notion of a Minkowski Lie algebra, which is the natural generalization of the notion of a real quadratic Lie algebra (metric Lie algebra). We then study the positive definite Minkowski Lie algebras and obtain a complete classification of the simple ones. Finally, we present some applications of our results to Finsler geometry and give a classification of bi-invariant Finsler metrics on Lie groups. This work was supported by NSFC (No.10671096) and NCET of China.     

Structurable Tori

The classification of structurable tori with nontrivial involution, which was begun by Allison and Yoshii, is completed. New examples of structurable tori are obtained using a construction of structurable algebras from a semilinear version of cubic forms satisfying the adjoint identity. The classification uses techniques borrowed from quadratic forms over ? ₂ and from the geometry of generalized quadrangles. Since structurable tori are the coordinate algebras for the centerless cores of extended affine Lie algebras of type BC₁, the results of this article provide a classification and new examples for this class of Lie algebras.     

Depth Generated Simple Lie Algebras

A Lie module algebra for a Lie algebra L is an algebra and L-module A such that L acts on A by derivations. The depth Lie algebra of a Lie algebra L with Lie module algebra A acts on a corresponding depth Lie module algebra . This determines a depth functor from the category of Lie module algebra pairs to itself. Remarkably, this functor preserves central simplicity. It follows that the Lie algebras corresponding to faithful central simple Lie module algebra pairs (A,L) with A commutative are simple. Upon iteration at such (A,L), the Lie algebras are simple for all i ∈ ω. In particular, the (i ∈ ω) corresponding to central simple Jordan Lie algops (A,L) are simple Lie algebras. Presented by Don Passman.     

紧致黎曼对称空间的全测地子流形及其稳定性Ⅱ

本文决定了经典的紧致黎曼对称空间的一大批全测地子流形,并确定了它们在其包围空间中的稳定性.     

Construction and classification of complex simple Lie algebras via projective geometry

We construct the complex simple Lie algebras using elementary algebraic geometry. We use our construction to obtain a new proof of the classification of complex simple Lie algebras that does not appeal to the classification of root systems.     

Complete Classification of BKM Lie Superalgebras Possessing Special Imaginary Roots

In this article, we give a complete classification of BKM Lie superalgebras possessing special imaginary roots. In this classification, we have also included infinite dimensional BKM Lie superalgebras with finite or infinite number of real or imaginary simple roots.