共查询到20条相似文献,搜索用时 15 毫秒
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Jin Ning 《数学学报(英文版)》1997,13(2):155-160
In this paper it is proved that any automorphism of an infinite dimensional Lie algebra of Cartan type over an algebraically
closed field of characteristicp>2 can be induced from an automorphism of the associated divided power algebra. 相似文献
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For an additive subgroup G of a field F of characteristic zero, a Lie algebra B(G) of Block type is defined with basis {Lα,i| α∈G, i∈Z+} and relations [Lα,i, Lβ,j] = (β-α)Lα+β,i+j+(αj-βi)Lα+β,Lα+β,i+j-1.It is proved that an irreducible highest weight B(Z)-module is quasifinite if and only if it is a proper quotient of a Verma module. Furthermore, for a total order λ on G and any ∧∈B(G)0^*(the dual space of B(G)0 = span{L0,i|i∈Z+}), a Verma B(G)-module M(∧,λ) is defined, and the irreducibility of M(A,λ) is completely determined. 相似文献
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Block introduced certain analogues of the Zassenhaus algebras over a field of characteristic 0. The nongraded infinite-dimensional simple Lie algebras of Block type constructed by Xu can be viewed as generalizations of the Block algebras. In this paper, we construct a family of irreducible modules in terms of multiplication and differentiation operators on "polynomials" for four-devivation nongraded Lie algebras of Block type based on the finite-dimensional irreducible weight modules with multiplicity one of general linear Lie algebras. We also find a new series of submodules from which some irreducible quotient modules are obtained. 相似文献
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In this paper we prove that there are no self-extensions of simple modules over restricted Lie algebras of Cartan type. The proof given by Andersen for classical Lie algebras not only uses the representation theory of the Lie algebra, but also representations of the corresponding reductive algebraic group. The proof presented in the paper follows in the same spirit by using the construction of a infinite-dimensional Hopf algebra D(G) u(
) containing u(
) as a normal Hopf subalgebra, and the representation theory of this algebra developed in our previous work. Finite-dimensional hyperalgebra analogs D(G
r
) u(
) have also been constructed, and the results are stated in this setting. 相似文献
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Highest weight representations of a Lie algebra of Block type 总被引:2,自引:0,他引:2
Yue-zhu WU & Yu-cai SU Department of Mathematics Shanghai Jiaotong University Shanghai China Department of Mathematics Qufu Normal University Qufu China Department of Mathematics University of Science Technology of China Hefei China 《中国科学A辑(英文版)》2007,50(4):549-560
For a field F of characteristic zero and an additive subgroup G of F, a Lie algebra B(G) of the Block type is defined with the basis {Lα,i, c|α∈G, -1≤i∈Z} and the relations [Lα,i,Lβ,j] = ((i 1)β- (j 1)α)Lα β,i j αδα,-βδi j,-2c,[c, Lα,i] = 0. Given a total order (?) on G compatible with its group structure, and anyα∈B(G)0*, a Verma B(G)-module M(A, (?)) is defined, and the irreducibility of M(A,(?)) is completely determined. Furthermore, it is proved that an irreducible highest weight B(Z )-module is quasifinite if and only if it is a proper quotient of a Verma module. 相似文献
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We compute the infinitesimal deformations of two families of restricted simple modular Lie algebras of Cartan-type: the Witt–Jacobson and the Special Lie algebras. 相似文献
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The simple modules with homogeneous characters are considered, their dimension formulas are determined.Presented by D. Passman. 相似文献
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The Lie algebra of Cartan type K which occurs as a subalgebra of the Lie algebra of derivations of the polynomial algebra F[x0, x1,…, xn,xn?1,…,x?n], where F is a field of characteristic 0, was generalized by the first author to a class which included a subalgebra of the derivations of the Laurent polynomials F[x0,x1,…, xn,x?1,…,x?n,X0 ?1x1 -1,…,xn ?1,…,x?1 ?1…,x?n ?1]A further generalization of these algebras is the main topic of this paper. We show when these algebras are simple, determine all possible 相似文献
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Mark Curtis Wilson 《Proceedings of the American Mathematical Society》1996,124(2):383-387
We show that a primeness criterion for enveloping algebras of Lie superalgebras discovered by Bell is applicable to the Cartan type Lie superalgebras , even. Other algebras are considered but there are no definitive answers in these cases.
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Salvatore Siciliano 《代数通讯》2013,41(12):4513-4522
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A locally convex Lie algebra is said to be locally exponential if it belongs to some local Lie group in canonical coordinates. In this note we give criteria
for locally exponential Lie algebras of vector fields on an infinite-dimensional manifold to integrate to global Lie group
actions. Moreover, we show that all necessary conditions are satisfied if the manifold is finite-dimensional connected and
σ-compact, which leads to a generalization of Palais’ Integrability Theorem.
相似文献
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In this article, we determine the Cartan invariants for Zassenhaus algebras W(1,n). This is done by reducing representations of generalized restricted Cartan type Lie algebra W(1,n) to representations of restricted Lie algebras W(1,1) and of ± b𝔰 ± b𝔩(2), and then extending Feldvoss-Nakano's argument on W(1,1) to the case W(1,n). 相似文献
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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
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Donald W. Barnes 《代数通讯》2019,47(8):3198-3201
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D. S. Shirokov 《Linear and Multilinear Algebra》2018,66(9):1870-1887
We give a full classification of Lie algebras of specific type in complexified Clifford algebras. These 16 Lie algebras are direct sums of subspaces of quaternion types. We obtain isomorphisms between these Lie algebras and classical matrix Lie algebras in the cases of arbitrary dimension and signature. We present 16 Lie groups: one Lie group for each Lie algebra associated with this Lie group. We study connection between these groups and spin groups. 相似文献
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In this paper, we use Block’s results to classify irreducible modules over the diamond Lie algebra 𝔇. As a corollary, we also give a classification of irreducible modules over the Euclidean algebra 𝔢(2). 相似文献