This paper is a continuation of [2]. We prove Conjecture 5.1 of [2] which gives a characterization of simple Lie algebras of finite dimension of type B2e, C2e, D2e＋1, E7 and Es in terms of some gradations of these al...This paper is a continuation of [2]. We prove Conjecture 5.1 of [2] which gives a characterization of simple Lie algebras of finite dimension of type B2e, C2e, D2e＋1, E7 and Es in terms of some gradations of these algebras over a field of characteristic 2.展开更多
In this paper,we give the notion of derivations of Lie 2-algebras using explicit formulas,and construct the associated derivation Lie 3-algebra.We prove that isomorphism classes of non-abelian extensions of Lie 2-alge...In this paper,we give the notion of derivations of Lie 2-algebras using explicit formulas,and construct the associated derivation Lie 3-algebra.We prove that isomorphism classes of non-abelian extensions of Lie 2-algebras are classified by equivalence classes of morphisms from a Lie 2-algebra to a derivation Lie 3-algebra.展开更多
In this paper, we study the structure theory of a class of not-finitely graded Lie alge- bras related to generalized Heisenberg-Virasoro algebras. In particular, the derivation algebras, the automorphism groups and th...In this paper, we study the structure theory of a class of not-finitely graded Lie alge- bras related to generalized Heisenberg-Virasoro algebras. In particular, the derivation algebras, the automorphism groups and the second cohomology groups of these Lie algebras are determined.展开更多
In this paper, M is a smooth manifold of finite dimension n, A is a local algebra and MA is the associated Weil bundle. We study Poisson vector fields on MA and we prove that all globally hamiltonian vector fields on ...In this paper, M is a smooth manifold of finite dimension n, A is a local algebra and MA is the associated Weil bundle. We study Poisson vector fields on MA and we prove that all globally hamiltonian vector fields on MA are Poisson vector fields.展开更多
文摘This paper is a continuation of [2]. We prove Conjecture 5.1 of [2] which gives a characterization of simple Lie algebras of finite dimension of type B2e, C2e, D2e＋1, E7 and Es in terms of some gradations of these algebras over a field of characteristic 2.
基金supported by National Natural Science Foundation of China(Grant Nos.11026046,11101179,10971071)Doctoral Fund of Ministry of Education of China(Grant No.20100061120096)the Fundamental Research Funds for the Central Universities(Grant No.200903294)
文摘In this paper,we give the notion of derivations of Lie 2-algebras using explicit formulas,and construct the associated derivation Lie 3-algebra.We prove that isomorphism classes of non-abelian extensions of Lie 2-algebras are classified by equivalence classes of morphisms from a Lie 2-algebra to a derivation Lie 3-algebra.
基金Supported by National Natural Science Foundation of China(Grant Nos.11431010,11371278 and 11271284)Shanghai Municipal Science and Technology Commission(Grant No.12XD1405000)
文摘In this paper, we study the structure theory of a class of not-finitely graded Lie alge- bras related to generalized Heisenberg-Virasoro algebras. In particular, the derivation algebras, the automorphism groups and the second cohomology groups of these Lie algebras are determined.
文摘In this paper, M is a smooth manifold of finite dimension n, A is a local algebra and MA is the associated Weil bundle. We study Poisson vector fields on MA and we prove that all globally hamiltonian vector fields on MA are Poisson vector fields.
