共查询到20条相似文献,搜索用时 15 毫秒
1.
ZHU Linsheng Department of Mathematics Changshu Institute of Technology Changshu China 《中国科学A辑(英文版)》2006,49(4):477-493
A Lie algebra endowed with a nondegenerate, symmetric, invariant bilinear form is called a quadratic Lie algebra. In this paper, the author investigates the structure of solvable quadratic Lie algebras, in particular, the solvable quadratic Lie algebras whose Cartan subalgebras consist of semi-simple elements, the author presents a procedure to construct a class of quadratic Lie algebras from the point of view of cohomology and shows that all solvable quadratic Lie algebras can be obtained in this way. 相似文献
2.
We study a type of left-invariant structure on Lie groups or, equivalently, on Lie algebras. We introduce obstructions to
the existence of a hypo structure, namely the five-dimensional geometry of hypersurfaces in manifolds with holonomy SU(3).
The choice of a splitting
\mathfrakg* = V1 ?V2 {\mathfrak{g}^*} = {V_1} \oplus {V_2} , and the vanishing of certain associated cohomology groups, determine a first obstruction. We also construct necessary conditions
for the existence of a hypo structure with a fixed almost-contact form. For nonunimodular Lie algebras, we derive an obstruction
to the existence of a hypo structure, with no choice involved. We apply these methods to classify solvable Lie algebras that
admit a hypo structure. 相似文献
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AbstractIn this article, solvable Leibniz algebras, whose nilradical is quasi-filiform Lie algebra of maximum length, are classified. The rigidity of such Leibniz algebras with two-dimensional complemented space to the nilradical is proved.Communicated by K. C. Misra 相似文献
4.
Dimension formula for graded Lie algebras and its applications 总被引:1,自引:0,他引:1
Seok-Jin Kang Myung-Hwan Kim 《Transactions of the American Mathematical Society》1999,351(11):4281-4336
In this paper, we investigate the structure of infinite dimensional Lie algebras graded by a countable abelian semigroup satisfying a certain finiteness condition. The Euler-Poincaré principle yields the denominator identities for the -graded Lie algebras, from which we derive a dimension formula for the homogeneous subspaces . Our dimension formula enables us to study the structure of the -graded Lie algebras in a unified way. We will discuss some interesting applications of our dimension formula to the various classes of graded Lie algebras such as free Lie algebras, Kac-Moody algebras, and generalized Kac-Moody algebras. We will also discuss the relation of graded Lie algebras and the product identities for formal power series.
5.
We classify certain non-linear Lie conformal algebras with three generators, which can be viewed as deformations of the current
Lie conformal algebra of sℓ
2. In doing so we discover an interesting 1-parameter family of non-linear Lie conformal algebras and the corresponding freely generated vertex algebras , which includes for d = 1 the affine vertex algebra of sℓ
2 at the critical level k = –2. We construct free-field realizations of the algebras extending the Wakimoto realization of at the critical level, and we compute their Zhu algebras.
Dedicated to our teacher Victor Kac on the occasion of his 65th birthday 相似文献
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E. Spiegel 《Linear and Multilinear Algebra》2004,52(2):115-120
We give conditions when a strictly upper triangular element of an incidence algebra over a commutative ring is the Lie commutator of two elements of the incidence algebra, one of which is strictly upper triangular. In particular, it follows that this is the case for the ring of n × n upper triangular matrices, where n is either finite or infinite. 相似文献
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Central extensions of some Lie algebras 总被引:5,自引:0,他引:5
We consider three Lie algebras: , the Lie algebra of all derivations on the algebra of formal Laurent series; the Lie algebra of all differential operators on ; and the Lie algebra of all differential operators on We prove that each of these Lie algebras has an essentially unique nontrivial central extension.
12.
C. Roger 《Theoretical and Mathematical Physics》2013,174(3):315-330
We describe some Lie algebras of the Kac-Moody type, construct their double extensions, central and by derivations; we also construct the corresponding Lie groups in some cases. We study the case of the Lie algebra of unimodular vector fields in more detail and use the linear Poisson structure on their regular duals to construct generalizations of some infinite-dimensional Hamiltonian systems, such as magnetohydrodynamics. 相似文献
13.
We generalize basic results relating the associated graded Lie algebra and the holonomy Lie algebra of a group, from finitely presented, commutator-relators groups to arbitrary finitely presented groups. Using the notion of “echelon presentation,” we give an explicit formula for the cup-product in the cohomology of a finite 2-complex. This yields an algorithm for computing the corresponding holonomy Lie algebra, based on a Magnus expansion method. As an application, we discuss issues of graded-formality, filtered-formality, 1-formality, and mildness. We illustrate our approach with examples drawn from a variety of group-theoretic and topological contexts, such as link groups, one-relator groups, and fundamental groups of orientable Seifert fibered manifolds. 相似文献
14.
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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V. M. Petrogradsky Yu. P. Razmyslov E. O. Shishkin 《Proceedings of the American Mathematical Society》2007,135(3):625-636
The wreath product of groups is one of basic constructions in group theory. We construct its analogue, a wreath product of Lie algebras.
Consider Lie algebras and over a field . Let be the universal enveloping algebra. Then has the natural structure of a Lie algebra, where the multiplication is defined via the comultiplication in . Also, acts by derivations on via the (left) coregular action. The semidirect sum we call the wreath product and denote by . As a main result, we prove that an arbitrary extension of Lie algebras can be embedded into the wreath product .
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可换环上一般线性李代数在几类典型李代数中的扩代数 总被引:1,自引:0,他引:1
研究典型李代数的子代数结构,利用矩阵方法决定了含幺可换环上n级一般线性李代数分别在2n级辛代数,2n级正交代数及2n 1级正交代数中的扩代数. 相似文献
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Czechoslovak Mathematical Journal - We introduce the notion of quasi-trace functions on Lie algebras. As applications we study realizations of 3-dimensional and 4-dimensional 3-Lie algebras. Some... 相似文献
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We establish Écalle’s mould calculus in an abstract Lie-theoretic setting and use it to solve a normalization problem, which covers several formal normal form problems in the theory of dynamical systems. The mould formalism allows us to reduce the Lie-theoretic problem to a mould equation, the solutions of which are remarkably explicit and can be fully described by means of a gauge transformation group. The dynamical applications include the construction of Poincaré–Dulac formal normal forms for a vector field around an equilibrium point, a formal infinite-order multiphase averaging procedure for vector fields with fast angular variables (Hamiltonian or not), or the construction of Birkhoff normal forms both in classical and quantum situations. As a by-product we obtain, in the case of harmonic oscillators, the convergence of the quantum Birkhoff form to the classical one, without any Diophantine hypothesis on the frequencies of the unperturbed Hamiltonians. 相似文献
19.
Let (B
i
)
i∈I
be a set of Lie algebras; let X be a free Lie algebra; let
* X be their free sum; let R be an ideal of F such that R ⋂ B
i
= 1 (i ∈ I); let V be a variety of Lie algebras such that V(R) is an ideal of F. Under some restrictions, we construct an embedding of F/V(R) into the verbal wreath product of a free algebra of the variety V with F/R.
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 10, No. 4, pp. 235–241, 2004. 相似文献
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