In this paper,we classify the simple uniformly bounded weight modules for the vector eld Lie algebra W1 of in nite rank.It turns out that any such modules are intermediate series modules.This result is very di erent f...In this paper,we classify the simple uniformly bounded weight modules for the vector eld Lie algebra W1 of in nite rank.It turns out that any such modules are intermediate series modules.This result is very di erent from the vector eld Lie algebra Wd of nite rank.展开更多
The simple modules for electrical Lie algebra of type D5 were investigated.The sufficient and necessary criteria of the simple Z-graded highest weight modules were established by means of determining the singular vect...The simple modules for electrical Lie algebra of type D5 were investigated.The sufficient and necessary criteria of the simple Z-graded highest weight modules were established by means of determining the singular vectors of the Verma modules.The simple highest weight module is isomorphic to either that for the symplectic Lie algebra sp4 or Verma module.展开更多
It is shown that the support of an irreducible weight module over the SchrSdinger-Virasoro Lie algebra with an infinite-dimensional weight space coincides with the weight lattice, and all nontrivial weight spaces of s...It is shown that the support of an irreducible weight module over the SchrSdinger-Virasoro Lie algebra with an infinite-dimensional weight space coincides with the weight lattice, and all nontrivial weight spaces of such a module are infinite-dimensional. As a by-product, it is obtained that every simple weight module over Lie algebra of this type with a nontrivial finite-dimensional weight space is a Harish-Chandra module.展开更多
We construct a class of modules for extended affine Lie algebra gl l（Cq） by using the free fields. A necessary and sufficient condition is given for those modules being irreducible.
For any module V over the two-dimensional non-abelian Lie algebra b and scalar a ∈C, we define a class of weight modules Fα（V） with zero central charge over the affine Lie algebra A（1）. These weight modules have...For any module V over the two-dimensional non-abelian Lie algebra b and scalar a ∈C, we define a class of weight modules Fα（V） with zero central charge over the affine Lie algebra A（1）. These weight modules have infinite- dimensional weight spaces if and only if V is infinite dimensional. In this paper, we will determine necessary and sufficient conditions for these modules Fα（V） to be irreducible. In this way, we obtain a lot of irreducible weight A1（1）-modules with infinite-dimensional weight spaces.展开更多
This article mainly discusses the direct sum decomposition of type G_2 Lie algebra, which, under such decomposition, is decomposed into a type A_1 simple Lie algebra and one of its modules. Four theorems are given to ...This article mainly discusses the direct sum decomposition of type G_2 Lie algebra, which, under such decomposition, is decomposed into a type A_1 simple Lie algebra and one of its modules. Four theorems are given to describe this module,which could be the direct sum of two or three irreducible modules, or the direct sum of weight modules and trivial modules, or the highest weight module.展开更多
Imaginary Verma modules, parabolic imaginary Verma modules, and Verma modules at level zero for double affine Lie algebras are constructed using three different triangular decompositions. Their relations are investiga...Imaginary Verma modules, parabolic imaginary Verma modules, and Verma modules at level zero for double affine Lie algebras are constructed using three different triangular decompositions. Their relations are investigated, and several results are generalized from the affine Lie algebras. In particular, imaginary highest weight modules, integrable modules, and irreducibility criterion are also studied.展开更多
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＋...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.展开更多
In this paper,we prove that the electrical Lie algebra e D_(5)is isomorphic to the semidirect product of sp_(4)and a 2-step nilpotent Lie algebra.Furthermore,we classify the irreducible highest weight modules for e D_...In this paper,we prove that the electrical Lie algebra e D_(5)is isomorphic to the semidirect product of sp_(4)and a 2-step nilpotent Lie algebra.Furthermore,we classify the irreducible highest weight modules for e D_(5).展开更多
For a field $\mathbb{F}$ of characteristic zero and an additive subgroup G of $\mathbb{F}$ , a Lie algebra B(G) of the Block type is defined with the basis {L α,i , c | α ∈ G ?1 ≤ i ∈ ?} and the relations [L α,i...For a field $\mathbb{F}$ of characteristic zero and an additive subgroup G of $\mathbb{F}$ , a Lie algebra B(G) of the Block type is defined with the basis {L α,i , c | α ∈ G ?1 ≤ i ∈ ?} and the relations [L α,i , L β,j ] = ((i + 1)β ? (j + 1)α)L α+β,i+j + αδ α, ?β δ i+j,?2 c, [c, L α,i ] = 0. Given a total order ? on G compatible with its group structure, and any Λ ∈ B(G) 0 * , a Verma B(G)-module M(Λ, ?) is defined, and the irreducibility of M(Λ, ?) is completely determined. Furthermore, it is proved that an irreducible highest weight B(?)-module is quasifinite if and only if it is a proper quotient of a Verma module.展开更多
文摘In this paper,we classify the simple uniformly bounded weight modules for the vector eld Lie algebra W1 of in nite rank.It turns out that any such modules are intermediate series modules.This result is very di erent from the vector eld Lie algebra Wd of nite rank.
基金Fundamental Research Funds for the Central Universities,China(No.2232021G13)。
文摘The simple modules for electrical Lie algebra of type D5 were investigated.The sufficient and necessary criteria of the simple Z-graded highest weight modules were established by means of determining the singular vectors of the Verma modules.The simple highest weight module is isomorphic to either that for the symplectic Lie algebra sp4 or Verma module.
基金Supported by China Postdoctoral Science Foundation Grant 20080440720, NSF Grants 10671027, 10825101 of China and ＂One Hundred Talents Program＂ from University of Science and Technology of China
文摘It is shown that the support of an irreducible weight module over the SchrSdinger-Virasoro Lie algebra with an infinite-dimensional weight space coincides with the weight lattice, and all nontrivial weight spaces of such a module are infinite-dimensional. As a by-product, it is obtained that every simple weight module over Lie algebra of this type with a nontrivial finite-dimensional weight space is a Harish-Chandra module.
基金supported by National Natural Science Foundation of China (Grant Nos.10726014, 10801010)
文摘We construct a class of modules for extended affine Lie algebra gl l（Cq） by using the free fields. A necessary and sufficient condition is given for those modules being irreducible.
基金The authors would like to thank the referees for nice suggestions. This work was supported in part by the National Natural Science Foundation of China （Grant No. 11301143） and the school fund of Henan University （yqpy20140044）.
文摘For any module V over the two-dimensional non-abelian Lie algebra b and scalar a ∈C, we define a class of weight modules Fα（V） with zero central charge over the affine Lie algebra A（1）. These weight modules have infinite- dimensional weight spaces if and only if V is infinite dimensional. In this paper, we will determine necessary and sufficient conditions for these modules Fα（V） to be irreducible. In this way, we obtain a lot of irreducible weight A1（1）-modules with infinite-dimensional weight spaces.
基金The CLRPF(17pzxmyb10) of Guangdong Peizheng College
文摘This article mainly discusses the direct sum decomposition of type G_2 Lie algebra, which, under such decomposition, is decomposed into a type A_1 simple Lie algebra and one of its modules. Four theorems are given to describe this module,which could be the direct sum of two or three irreducible modules, or the direct sum of weight modules and trivial modules, or the highest weight module.
基金N. Jing＇s work was partially supported by the Simons Foundation （Grant No. 198129） and the National Natural Science Foundation of China （Grant No. 11271138）, and he also acknowledged the hospitality of Max-Planck Institute for Mathematics in the Sciences at Leipzig during this work.
文摘Imaginary Verma modules, parabolic imaginary Verma modules, and Verma modules at level zero for double affine Lie algebras are constructed using three different triangular decompositions. Their relations are investigated, and several results are generalized from the affine Lie algebras. In particular, imaginary highest weight modules, integrable modules, and irreducibility criterion are also studied.
基金NSF Grant No.10471091 of Chinathe Grant of"One Hundred Talents Program"from the University of Science and Technology of China
文摘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.
基金Supported by the Fundamental Research Funds for the Central Universities(Grant No.2232021G-13).
文摘In this paper,we prove that the electrical Lie algebra e D_(5)is isomorphic to the semidirect product of sp_(4)and a 2-step nilpotent Lie algebra.Furthermore,we classify the irreducible highest weight modules for e D_(5).
基金This work was supported by the National Natural Science Foundation of China (Grant No. 10471096) and One Hundred Talents Program from University of Science and Technology of China
文摘For a field $\mathbb{F}$ of characteristic zero and an additive subgroup G of $\mathbb{F}$ , a Lie algebra B(G) of the Block type is defined with the basis {L α,i , c | α ∈ G ?1 ≤ i ∈ ?} and the relations [L α,i , L β,j ] = ((i + 1)β ? (j + 1)α)L α+β,i+j + αδ α, ?β δ i+j,?2 c, [c, L α,i ] = 0. Given a total order ? on G compatible with its group structure, and any Λ ∈ B(G) 0 * , a Verma B(G)-module M(Λ, ?) is defined, and the irreducibility of M(Λ, ?) is completely determined. Furthermore, it is proved that an irreducible highest weight B(?)-module is quasifinite if and only if it is a proper quotient of a Verma module.
