共查询到16条相似文献,搜索用时 93 毫秒
1.
The main purpose of the present paper is to give some properties of the Jacobson radical,the Frattini subsystem and c-ideals of a Lie triple system.Some further results concerning the Frattini subsystems of nilpotent and solvable Lie triple systems are obtained.Moreover,we develop initially c-ideals for a Lie triple system and make use of them to give some characterizations of a solvable Lie triple system. 相似文献
2.
As a natural generalization of a restricted Lie algebra, a restricted Lie triple system was defined by Hodge. In this paper, we develop initially the Frattini theory for restricted Lie triple systems, generalize some results of Frattini p-subalgebra for restricted Lie algebras, obtain some properties of the Frattini p-subsystem and give the relationship between Фp(T) and Ф(T) for solvable Lie triple systems. 相似文献
3.
In this article, we discuss some properties of a supersymmetric invariant bilinear form on Lie supertriple systems. In particular, a supersymmetric invariant bilinear form on Lie supertriple systems can be extended to its standard imbedding Lie superalgebras. Furthermore, we generalize Garland's theory of universal central extensions for Lie supertriple systems following the classical one for Lie superalgebras. We solve the problems of lifting automorphisms and lifting derivations. 相似文献
4.
In this article, the Killing form of a Lie supertriple system (LSTS) and that of its imbedding Lie superalgebra (LSA) are investigated, and a unique decomposition theorem for a quasiclassical LSTS with trivial center is established by means of the parallel decomposition theorem for a quasiclassical LSA. 相似文献
5.
For Lie triple systems in the characteristic zero setting, we obtain by means of the Killing forms two criterions for semisimplicity and for solvability respectively, and then investigate the relationship among the Killing forms of a real Lie triple system To, the complexification T of To, and the realification of T. 相似文献
6.
Jianqiang Feng 《数学研究通讯:英文版》2012,28(1):91-96
For a Lie triple system T over a field of characteristic zero, some sufficient conditions for T to be two-generated are proved. We also discuss to what extent the two-generated subsystems determine the structure of the system T . One of the main results is that T is solvable if and only if every two elements generates a solvable subsystem. In fact, we give an explicit two-generated law for the two-generated subsystems. 相似文献
7.
With the help of a Lie algebra,two kinds of Lie algebras with the forms of blocks are introduced for generating nonlinear integrable and bi-integrable couplings.For illustrating the application of the Lie algebras,an integrable Hamiltonian system is obtained,from which some reduced evolution equations are presented.Finally,Hamiltonian structures of nonlinear integrable and bi-integrable couplings of the integrable Hamiltonian system are furnished by applying the variational identity.The approach presented in the paper can also provide nonlinear integrable and bi-integrable couplings of other integrable system. 相似文献
8.
9.
We introduce elementary and Φ-free Lie triple systems and study the properties of these systems.In particular,structures of subsystems of an elementary Lie triple system and a class of Φ-free Lie triple systems are investigated. 相似文献
10.
In this article,we study the Lie supertriple system(LSTS)T over a field K admitting a nondegenerate invariant supersymmetric bilinear form(call such a T metrisable).We give the definition of T_ω~*-extension of an LSTS T,prove a necessary and sufficient condition for a metrised LSTS(T,φ)to be isometric to a T~*-extension of some LSTS,and determine when two T~*-extensions of an LSTS are"same",i.e.,they are equivalent or isometrically equivalent. 相似文献
11.
该文首先研究了李超三系的中心、导子超代数和内导子超代数的分解问题, 给出了具有平凡中心的李超三系的分解唯一性定理, 同时讨论了李超三系的自同构的扩张. 相似文献
12.
讨论了二次李超三系的唯一分解,得到了二次李超三系分解为非退化不可约阶化理想的分解定理. 相似文献
13.
In this article, we discuss some properties of a supersymmetric invariant bilinear form on Lie supertriple systems. In particular, a supersymmetric invariant bilinear form on Lie supertriple systems can be extended to its standard imbedding Lie superalgebras. Furthermore, we generalize Garland's theory of universal central extensions for Lie supertriple systems following the classical one for Lie superalgebras. We solve the problems of lifting automorphisms and lifting derivations. 相似文献
14.
15.
Jianqiang Feng 《数学研究通讯:英文版》2014,30(1):51-59
In this article, we study the Lie supertriple system (LSTS) $T$ over a field$\mathbb{K}$ admitting a nondegenerate invariant supersymmetric bilinear form (call such a $T$ metrisable). We give the definition of $T^∗_ω$-extension of an LSTS $T$, prove a necessary
and sufficient condition for a metrised LSTS ($T$, $ϕ$) to be isometric to a $T^∗$-extension
of some LSTS, and determine when two $T^∗$-extensions of an LSTS are "same", i.e.,
they are equivalent or isometrically equivalent. 相似文献
16.
研究了限制李三系的半单元的一些重要性质,给出了若干个限制李三系是可换的条件,得到了限制李三系的有环面元基的几个条件,刻划了限制李三系的Frattini p-子系的一些性质.同时,研究了中心为零的所有元素是半单元的限制李三系的一些重要性质. 相似文献