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1.
Anselm Eggert 《Semigroup Forum》1990,41(1):115-121
This paper gives some basic facts on Lie semialgebras and shows the crucial steps that lead to a classification of semialgebras
in a class of Lie algebras that contains the reductive ones. The classification of invariant wedges by Hilgert and Hofmann
is a prerequisite.
This paper was presented at the Conference on “The analytical and topological theory of semigroups” in Oberwolfach, January
29 through February 4, 1989 相似文献
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《代数通讯》2013,41(9):3157-3178
ABSTRACT Pairs (A, L) with A a commutative algebra and L a Lie algebra acting on A by derivations, called Lie algops, are studied as algebraic structures over arbitrary fields of arbitrary characteristic. Lie algops possess modules and tensor products—and are considered with respect to a central simple theory. The simplicity problem of determining the faithful unital simple Lie algops ( A, L ) is of interest since the corresponding Lie algebras AL are usually simple (Jordan, 2000). For locally finite Lie algops, and up to purely inseparable descent, this problem reduces by way of closures to the closed central simplicity problem of determining those which are closed central simple. The simplicity and representation theories for locally nilpotent separably triangulable unital Lie algops are of particular interest because they relate to the problems of classifying simple Lie algebras of Witt type and their representations. Of these, the simplicity theory reduces to that of Jordan Lie algops. The main Theorems 7.3 and 7.4 reduce the simplicity and representation theories for Jordan Lie algops to the simplicity and representation theories for simple nil and toral Lie algops. 相似文献
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Enrique Macias Virgós 《Annals of Global Analysis and Geometry》1993,11(1):35-40
We obtain several homotopy obstructions to the existence of non-closed connected Lie subgroupsH in a connected Lie groupG.First we show that the foliationF(G, H) onG determined byH is transversely complete [4]; moreover, forK the closure ofH inG, F(K, H) is an abelian Lie foliation [2].Then we prove that 1(K) and 1(H) have the same torsion subgroup,
n
(K)=
n
(H) for alln 2, and rank1(K) — rank1(H) > codimF(K, H). This implies, for instance, that a contractible (e.g. simply connected solvable) Lie subgroup of a compact Lie group must be abelian. Also, if rank1(G) 1 then any connected invariant Lie subgroup ofG is closed; this generalizes a well-known theorem of Mal'cev [3] for simply connected Lie groups.Finally, we show that the results of Van Est on (CA) Lie groups [6], [7] provide many interesting examples of such foliations. Actually, any Lie group with non-compact centre is the (dense) leaf of a foliation defined by a closed 1-form. Conversely, when the centre is compact, the latter is true only for (CA) Lie groups (e.g. nilpotent or semisimple). 相似文献
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孟道骥等对完备李代数作了系统的研究并已获得很多基本和重要的结果。本文给出完备李群与完备李代数的某些关系。 相似文献
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In this paper we introduce new generalized fuzzy Lie ideals of Lie algebras and study some of their important properties.We characterize these generalized Lie ideals of Lie algebras by their level subsets.Some characterization of the generalized fuzzy Lie ideals of Lie algebras are also established. 相似文献
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A special symplectic Lie group is a triple ${(G,\omega,\nabla)}$ such that G is a finite-dimensional real Lie group and ω is a left invariant symplectic form on G which is parallel with respect to a left invariant affine structure ${\nabla}$ . In this paper starting from a special symplectic Lie group we show how to “deform” the standard Lie group structure on the (co)tangent bundle through the left invariant affine structure ${\nabla}$ such that the resulting Lie group admits families of left invariant hypersymplectic structures and thus becomes a hypersymplectic Lie group. We consider the affine cotangent extension problem and then introduce notions of post-affine structure and post-left-symmetric algebra which is the underlying algebraic structure of a special symplectic Lie algebra. Furthermore, we give a kind of double extensions of special symplectic Lie groups in terms of post-left-symmetric algebras. 相似文献
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《数学的实践与认识》2019,(23)
对filiform李代数R_n的triple导子进行了研究.利用triple导子的定义,通过计算线性变换在一组特殊的基上的作用结果,得到了filiform李代数R_n的triple导子的矩阵形式,并发现其triple导子代数是一个维数为2n-1的可解李代数. 相似文献
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KAREL Dekimpe 《Compositio Mathematica》2000,121(2):183-204
In this paper, we study polynomial structures by starting on the Lie algebra level, thenpassing to Lie groups to finally arrive at the polycyclic-by-finite group level. To be more precise,we first show how a general solvable Lie algebra can be decomposed into a sum of two nilpotentsubalgebras. Using this result, we construct, for any simply connected, connected solvable Lie groupG of dim n, a simply transitive action on R
n which is polynomial and of degree n3. Finally, we show the existence of a polynomial structure on any polycyclic-by-finite group , which is of degree h()3 on almost the entire group (h () being the Hirsch length of ). 相似文献
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Peter Bubenik 《Journal of Pure and Applied Algebra》2008,212(2):401-410
A simply connected topological space X has homotopy Lie algebra π∗(ΩX)⊗Q. Following Quillen, there is a connected differential graded free Lie algebra (dgL) called a Lie model, which determines the rational homotopy type of X, and whose homology is isomorphic to the homotopy Lie algebra. We show that such a Lie model can be replaced with one that has a special property that we call being separated. The homology of a separated dgL has a particular form which lends itself to calculations. 相似文献
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LiangYun Zhang 《中国科学A辑(英文版)》2008,51(6):1017-1026
In this paper,we first give a direct sum decomposition of Lie comodules,and then accord- ing to the Lie comodule theory,construct some(triangular)Lie bialgebras through Lie coalgebras. 相似文献
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D. V. Alekseevskii 《Journal of Mathematical Sciences》1985,28(6):924-949
The survey deals with the investigations reviewed inReferativnyi Zhurnal Matematika between 1977–1981. In the survey there are reflected the investigations on the structure of Lie groups and Lie algebras, on their finite-dimensional linear representations and universal enveloping algebras, on the theory of invariants and Lie groups of transformations, and also on continuous and discrete subgroups of Lie groups.Translated from Itogi Nauki i Tekhniki, Seriya Algebra, Topologiya, Geometriya, Vol. 20, No. 153–192, 1982. 相似文献
20.
D. A. Leites 《Journal of Mathematical Sciences》1985,30(6):2481-2512
Results pertaining to the theory of representations of classical Lie superalgebras are collected in the survey.Translated from Itogi Nauki i Tekhniki, Seriya Sovremennye Problemy Matematiki, Noveishie Dostizheniya, Vol. 25, pp. 3–50, 1984. 相似文献