3. The restriction Pr|Fi:(Fi,+,×)→(H,⊕,⊗) is a Lie algebra homomorphism, i=1,2,⋯, then (F,Pr,H) is called a bundled Lie sub-algebra of (E,Pr,B). It is well known that there are some useful Lie sub-algebras of Lie algebra gl(n,R). When gl(n,R), ∀n, ...
Lie algebra theory is to a large extend the classification of the semisimple Lie algebras which are direct sums of the simple algebras listed in the previous paragraph, i.e. to show that those are all simple Lie algebras there are.
The main application of the existence and properties of the BBW type parabolic subalgebras is our verification of the following theorem. Theorem 1.2.1 Let g be a simple classical Lie superalgebra and let M be in F(g,g0¯). The aforementioned theorem has been a conjecture that was first ...
That is, Lie groups with isomorphic Lie algebras are not necessarily isomorphic, and the issue here is the usual simply-connectedness. However, it seems that in (a) we are perfectly able to distinguish the different Lie groups with a given Lie algebra. Question(s) Where is the topological...
The Lie algebra gl3(Cq) is an extended affine Lie algebra of type A2 with nullity 2. (See [AABGP] and [BGK] for definitions). Extended affine Lie algebras are a higher dimensional generalization of affine KacMoody Lie algebras introduced by [H-KT] and systematically studied in [AABGP] ...
应用.Toroidal 仿射Knc—Moody Lie代数的齐次顶点表示 Lie代数的自然推广.在【MRY】和【RM】里,单边toroidal 被构造出来.这个构造是仿射Kac.Moody 在第7章,我们构造出G2型的toroidalLie代数以及放射Leibzfiz代数的这种顶点算子表示. 旦Q△蟹垡型 英 文 摘 要 Leibniz andassociative as ofLie as— algebras ...
The non-decomposable non-Abelian(n+2)-dimensional maximal rank nilpotent n-Lie algebras are investigated. 根据最大秩幂零n-Lie代数的概念及有关结论,证明不可分解非Abel最大秩幂零的n+2维n-Lie代数在同构意义下只有一类,给出了具体的乘法表,并讨论了它的导子代数及其内导子代数。 3. In this paper...
We initiate a study on a range of new generalized derivations of finite-dimensional Lie algebras over an algebraically closed field of characteristic zero. This new generalization of derivations has an analogue in the theory of associative prime rings and unites many well-known generalized derivations...
The generators of the Lie algebra of the general linear group GL( n, R) and of the special linear group SL( n, R) are, recurrently, expressed through polynomials in the quantum canonical variables p t and q t. These realizations are skew-Hermitian, the Casimir operations are realized by...
In section 5, we give all Rota-Baxter operators on 2-dimensional complex pre-Lie algebras. In section 6, some examples in higher dimensions are given. In section 7, we give some further discussion and questions. Throughout this paper, without special saying, all algebras are of finite ...