共查询到20条相似文献,搜索用时 10 毫秒
1.
2.
3.
4.
文章利用有单位元且2,3是单位的交换环的极大理想刻画了其上特殊线性李代数包含典范环面的极大子代数.确定了特殊线性李代数极大子代数的个数,并证明了每个极大子代数均可通过置换矩阵共轭于标准的极大子代数. 相似文献
5.
6.
7.
Let K be a field of characteristic p>0 and let KG be the group algebra of an arbitrary group G over K. It is known that if KG is Lie nilpotent, then its lower as well as upper Lie nilpotency index is at least p+1. The group algebras KG for which these indices are p+1 or 2p or 3p?1 or 4p?2 have already been determined. In this paper, we classify the group algebras KG for which the upper Lie nilpotency index is 5p?3, 6p?4 or 7p?5. 相似文献
8.
The paper studies the existence of closed invariant subspaces for a Lie algebra L of bounded operators on an infinite-dimensional Banach space X. It is assumed that L contains a Lie subalgebra L0 that has a non-trivial closed invariant subspace in X of finite codimension or dimension. It is proved that L itself has a non-trivial closed invariant subspace in the following two cases: (1) L0 has finite codimension in L and there are Lie subalgebras L0=L0⊂L1⊂?⊂Lp=L such that Li+1=Li+[Li,Li+1] for all i; (2) L0 is a Lie ideal of L and dim(L0)=∞. These results are applied to the problem of the existence of non-trivial closed Lie ideals and closed characteristic Lie ideals in an infinite-dimensional Banach Lie algebra L that contains a non-trivial closed Lie subalgebra of finite codimension. 相似文献
9.
In this paper we study the complete reducibility of representations of infinite-dimensional Lie algebras from the perspective of representation theory of vertex algebras. 相似文献
10.
F. J. Echarte M. C. Márquez J. Núñez 《Bulletin of the Brazilian Mathematical Society》2005,36(1):59-77
In this paper we generalize naturally graded filiform Lie algebras as well as filiform Lie algebras admitting a connected gradation of maximal length, by introducing the concept of c-graded complex filiform Lie algebras. We deal with the particular case of 3-graded filiform Lie algebras and we obtain their classification in arbitrary dimension. We finally show a link among derived algebras, graded filiform and rigid solvable Lie algebras. 相似文献
11.
12.
Let gln(R) be the general linear Lie algebra of all n × n matrices over a unital commutative ring R with 2 invertible, dn(R) be the Cartan subalgebra of gln(R) of all diagonal matrices. The maximal subalgebras of gln(R) that contain dn(R) are classified completely. 相似文献
13.
The aim of this work is to characterize the families of Frobenius (respectively, contact) solvable Lie algebras that satisfies the following condition: 𝔤 = 𝔥?V, where 𝔥?𝔤𝔩(V), |dim V?dim 𝔤|≤1 and NilRad(𝔤) = V, V being a finite dimensional vector space. In particular, it is proved that every complex Frobenius solvable Lie algebra is decomposable, whereas that in the real case there are only two indecomposable Frobenius solvable Lie algebras. 相似文献
14.
On split Lie algebras with symmetric root systems 总被引:1,自引:1,他引:0
Antonio J. Calderón Martín 《Proceedings Mathematical Sciences》2008,118(3):351-356
We develop techniques of connections of roots for split Lie algebras with symmetric root systems. We show that any of such
algebras L is of the form L = + Σ
j
I
j
with
a subspace of the abelian Lie algebra H and any I
j
a well described ideal of L, satisfying [I
j
, I
k
] = 0 if j ≠ k. Under certain conditions, the simplicity of L is characterized and it is shown that L is the direct sum of the family of its minimal ideals, each one being a simple split Lie algebra with a symmetric root system
and having all its nonzero roots connected. 相似文献
15.
Hideto Asashiba 《Mathematische Zeitschrift》2008,259(4):713-754
For each simply-laced Dynkin graph Δ we realize the simple complex Lie algebra of type Δ as a quotient algebra of the complex
degenerate composition Lie algebra of a domestic canonical algebra A of type Δ by some ideal I of that is defined via the Hall algebra of A, and give an explicit form of I. Moreover, we show that each root space of has a basis given by the coset of an indecomposable A-module M with root easily computed by the dimension vector of M.
Dedicated to Professor Claus Michael Ringel on the occasion of his 60th birthday. 相似文献
16.
N. Yu. Makarenko 《Siberian Mathematical Journal》2007,48(1):95-111
We prove that if a (?/n?)-graded Lie algebra L = ? i=0 n?1 L i has d nontrivial components L i and the null component L 0 has finite dimension m, then L has a homogeneous solvable ideal of derived length bounded by a function of d and of codimension bounded by a function of m and d. An analogous result holds also for the (?/n?)-graded Lie rings L = ? i=0 n?1 with few nontrivial components L i if the null component L 0 has finite order m. These results generalize Kreknin’s theorem on the solvability of the (?/n?)-graded Lie rings L = ? i=0 n?1 L i with trivial component L 0 and Shalev’s theorem on the solvability of such Lie rings with few nontrivial components L i . The proof is based on the method of generalized centralizers which was created by E. I. Khukhro for Lie rings and nilpotent groups with almost regular automorphisms of prime order [1], as well as on the technique developed in the work of N. Yu. Makarenko and E. I. Khukhro on the almost solvability of Lie algebras with an almost regular automorphism of finite order [2]. 相似文献
17.
Brbara Pogorelsky 《Journal of Algebra》2009,322(7):2335-2354
In this paper we describe the right coideal subalgebras containing all group-like elements of the multiparameter quantum group , where is a simple Lie algebra of type G2, while the main parameter of quantization q is not a root of 1. If the multiplicative order t of q is finite, t>4, t≠6, then the same classification remains valid for homogeneous right coideal subalgebras of the positive part of the multiparameter version of the small Lusztig quantum group. 相似文献
18.
Fangyan Lu 《Proceedings of the American Mathematical Society》2003,131(12):3883-3892
Let be a subalgebra of a nest algebra . If contains all rank one operators in , then is said to be large; if the set of rank one operators in coincides with that in the Jacobson radical of , is said to be radical-type. In this paper, algebraic isomorphisms of large subalgebras and of radical-type subalgebras are characterized. Let be a nest of subspaces of a Hilbert space and be a subalgebra of the nest algebra associated to (). Let be an algebraic isomorphism from onto . It is proved that is spatial if one of the following occurs: (1) () is large and contains a masa; (2) () is large and closed; (3) () is a closed radical-type subalgebra and ( is quasi-continuous (i.e. the trivial elements of are limit points); (4) () is large and one of and is not quasi-continuous.
19.
20.
A new characterization of semisimple Lie algebras 总被引:4,自引:0,他引:4
Said Benayadi 《Proceedings of the American Mathematical Society》1997,125(3):685-688
Using Casimir elements, we characterize the semisimple Lie algebras among the quadratic Lie algebras. This characterization gives, in particular, a generalization of a consequence of Cartan's second criterion.