共查询到20条相似文献,搜索用时 78 毫秒
1.
We obtain conditions for the nilpotency of finite-dimensional n-tuple Lie algebras and finite-dimensional associative n-tuple algebras. The established conditions are analogous to theorems of Engel and Wedderburn for Lie algebras and associative
algebras. 相似文献
2.
We prove an analog of the Lie theorem for finite-dimensional n-tuple solvable Lie algebras over an algebraically closed field of characteristic 0. 相似文献
3.
We study properties of n-tuple algebras of associative type. We show that the nilpotency of an n-tuple algebra of associative type is determined by the nilpotency of each element. In addition, we characterize the nilpotency of an n-tuple algebra of associative type in terms of the trace function. In the final part of the paper, we show that a homogeneously semisimple n-tuple algebra of associative type is the direct sum of two-sided ideals each of which is a homogeneously simple n-tuple algebra of associative type. 相似文献
4.
We say that a Lie algebra g is quasi-state rigid if every Ad-invariant continuous Lie quasi-state on it is the directional derivative of a homogeneous quasimorphism. Extending work of Entov and Polterovich, we show that every reductive Lie algebra, as well as the algebras C n ? u( n), n ≥ 1, are rigid. On the other hand, a Lie algebra which surjects onto the three-dimensional Heisenberg algebra is not rigid. For Lie algebras of dimension ≤ 3 and for solvable Lie algebras which split over a codimension one abelian ideal, we show that this is the only obstruction to rigidity. 相似文献
5.
It is well-known that there exists a close link between Lie Theory and Relativity Theory. Indeed, the set of all symmetries of the metric in our four-dimensional spacetime is a Lie group. In this paper we try to study this link in depth, by dealing with three particular types of Lie algebras: hn algebras, gn algebras and Heisenberg algebras. Our main goal is to compute the maximal abelian dimensions of each of them, which will allow us to move a step forward in the advancement of this subject. 相似文献
7.
Let \(\mathfrak{q}\)( n) be a simple strange Lie superalgebra over the complex field ?. In a paper by A.Ayupov, K.Kudaybergenov (2016), the authors studied the local derivations on semi-simple Lie algebras over ? and showed the difference between the properties of local derivations on semi-simple and nilpotent Lie algebras. We know that Lie superalgebras are a generalization of Lie algebras and the properties of some Lie superalgebras are similar to those of semi-simple Lie algebras, but \(\mathfrak{p}\)( n) is an exception. In this paper, we introduce the definition of the local superderivation on \(\mathfrak{q}\)( n), give the structures and properties of the local superderivations of \(\mathfrak{q}\)( n), and prove that every local superderivation on \(\mathfrak{q}\)( n), n > 3, is a superderivation. 相似文献
8.
The only known examples of Anosov diffeomorphisms are hyperbolic automorphisms of infranilmanifolds, and the existence of such automorphisms is a really strong condition on the rational nilpotent Lie algebra determined by the lattice, so called an Anosov Lie algebra. We prove that n⊕?⊕ n ( s times, s≥2) has an Anosov rational form for any graded real nilpotent Lie algebra n having a rational form. We also obtain some obstructions for the types of nilpotent Lie algebras allowed, and use the fact that the eigenvalues of the automorphism are algebraic integers (even units) to show that the types (5,3) and (3,3,2) are not possible for Anosov Lie algebras. 相似文献
11.
We obtain some general results on Sasakian Lie algebras and prove as a consequence that a (2 n + 1)-dimensional nilpotent Lie group admitting left-invariant Sasakian structures is isomorphic to the real Heisenberg group H 2n + 1. Furthermore, we classify Sasakian Lie algebras of dimension five and determine which of them carries a Sasakian α-Einstein structure. We show that a five-dimensional solvable Lie group with a left-invariant Sasakian structure and which admits a compact quotient by a discrete subgroup is isomorphic to either H 5 or a semidirect product ? ? ( H 3 × ?). In particular, the compact quotient is an S 1-bundle over a four-dimensional Kähler solvmanifold. 相似文献
12.
This work shows how to associate the Lie algebra hn, of upper triangular matrices, with a specific combinatorial structure of dimension 2, for n∈ N. The properties of this structure are analyzed and characterized. Additionally, the results obtained here are applied to obtain faithful representations of solvable Lie algebras. 相似文献
13.
The present paper is devoted to the classification of infinite-dimensional naturally graded Lie algebras that are narrow in the sense of Zelmanov and Shalev [9]. Such Lie algebras are Lie algebras of slow linear growth. In the theory of nonlinear hyperbolic partial differential equations the notion of the characteristic Lie algebra of equation is introduced [3]. Two graded Lie algebras n1 and n2 from our list, that are positive parts of the affine Kac–Moody algebras A1(1) and A2(2), respectively, are isomophic to the characteristic Lie algebras of the sinh-Gordon and Tzitzeika equations [6]. We also note that questions relating to narrow and slowly growing Lie algebras have been extensively studied in the case of a field of positive characteristic [2]. 相似文献
14.
Differential-difference equations of the form u? n = F n ( t, un?1, u n , un+1, u?n?1, u? n , u?n+1) are classified according to their intrinsic Lie point symmetries, equivalence group and some low-dimensional Lie algebras including the Abelian symmetry algebras, nilpotent nonAbelian symmetry algebras, solvable symmetry algebras with nonAbelian nilradicals, solvable symmetry algebras with Abelian nilradicals and nonsolvable symmetry algebras. Here F n is a nonlinear function of its arguments and the dot over u denotes differentiation with respect to t. 相似文献
15.
The present paper is devoted to the study of n-tuple semigroups. A free n-tuple semigroup of arbitrary rank is constructed and, as a consequence, singly generated free n-tuple semigroups are characterized. Moreover, examples of n-tuple semigroups are presented, the independence of the n-tuple semigroup axioms is proved, and it is shown that the natural semigroups of the constructed free n-tuple semigroup are isomorphic and the automorphism group of this n-tuple semigroup is isomorphic to a symmetric group. 相似文献
16.
We define a new invariant of quadratic Lie algebras and give a complete study and classification of singular quadratic Lie algebras, i.e. those for which the invariant does not vanish. The classification is related to O( n)-adjoint orbits in $\mathfrak{o}(n)$ . 相似文献
17.
We consider families of linear, parabolic PDEs in n dimensions which possess Lie symmetry groups of dimension at least four. We identify the Lie symmetry groups of these equations with the (2 n+1)-dimensional Heisenberg group and SL(2, R). We then show that for PDEs of this type, the Lie symmetries may be regarded as global projective representations of the symmetry group. We construct explicit intertwining operators between the symmetries and certain classical projective representations of the symmetry groups. Banach algebras of symmetries are introduced. 相似文献
18.
In the paper, the Lie algebras of infinitesimal H-projective transformations with 2n-dimensional Kähler manifolds of constant holomorphic sectional curvature are considered. It is proved that these algebras are isomorphic to the realification of the complex Lie algebra $sl(n, \mathbb{C})$ , and their local realization in the form of an algebra of vector fields on a manifold is described. 相似文献
19.
We construct all solvable Lie algebras with a specific n-dimensional nilradical nn,3 which contains the previously studied filiform ( n-2)-dimensional nilpotent algebra nn-2,1 as a subalgebra but not as an ideal. Rather surprisingly it turns out that the classification of such solvable algebras can be deduced from the classification of solvable algebras with the nilradical nn-2,1. Also the sets of invariants of coadjoint representation of nn,3 and its solvable extensions are deduced from this reduction. In several cases they have polynomial bases, i.e. the invariants of the respective solvable algebra can be chosen to be Casimir invariants in its enveloping algebra. 相似文献
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