Strongly irreducible submodules of modules are defined as follows： A submodule N of an Rmodule M is said to be strongly irreducible if for submodules L and K of M, the inclusion L ∩ K ∈ N implies that either L ∈ N...Strongly irreducible submodules of modules are defined as follows： A submodule N of an Rmodule M is said to be strongly irreducible if for submodules L and K of M, the inclusion L ∩ K ∈ N implies that either L ∈ N or K ∈ N. The relationship among the families of irreducible, strongly irreducible, prime and primary submodules of an R-module M is considered, and a characterization of Noetherian modules which contain a non-prime strongly irreducible submodule is given.展开更多
In this note the authors investigates the property of the GF(2)-modules for the wreath products Sz(q)wrCt,and establish some sufficient condition for a Sz(q)wrCt, GF(2)-module to be natural.
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
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
The near-group rings are an important class of fusion rings in the theory of tensor categories. In this paper, the irreducible Z＋-modules over the near-group fusion ring K（Z3, 3） are explicitly classified. It turns...The near-group rings are an important class of fusion rings in the theory of tensor categories. In this paper, the irreducible Z＋-modules over the near-group fusion ring K（Z3, 3） are explicitly classified. It turns out that there are only four inequivalent irreducible Z＋-modules of rank 2 and two inequivalent irreducible Z＋-modules of rank 4 over K（Z3, 3）.展开更多
We construct a class of modules for extended affne Lie algebra ■ by using the free fields. A necessary and sufficient condition is given for those modules being irreducible.
A monomial basis and a filtration of subalgebras for the universal enveloping algebra U（gl） of a complex simple Lie algebra gl of type Bl and Cl are given, and the decomposition of the Weyl module V （λ） as a U（g...A monomial basis and a filtration of subalgebras for the universal enveloping algebra U（gl） of a complex simple Lie algebra gl of type Bl and Cl are given, and the decomposition of the Weyl module V （λ） as a U（gl）-module into a direct sum of Weyl modules V （μ）’s as U（gl-1）modules is described. In particular, a new multiplicity formula for the Weyl module V （λ） is obtained in this note.展开更多
文摘Strongly irreducible submodules of modules are defined as follows： A submodule N of an Rmodule M is said to be strongly irreducible if for submodules L and K of M, the inclusion L ∩ K ∈ N implies that either L ∈ N or K ∈ N. The relationship among the families of irreducible, strongly irreducible, prime and primary submodules of an R-module M is considered, and a characterization of Noetherian modules which contain a non-prime strongly irreducible submodule is given.
文摘In this note the authors investigates the property of the GF(2)-modules for the wreath products Sz(q)wrCt,and establish some sufficient condition for a Sz(q)wrCt, GF(2)-module to be natural.
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This work was supported in part by the National Natural Science Foundation of China （Grant No. 11471282）.
文摘The near-group rings are an important class of fusion rings in the theory of tensor categories. In this paper, the irreducible Z＋-modules over the near-group fusion ring K（Z3, 3） are explicitly classified. It turns out that there are only four inequivalent irreducible Z＋-modules of rank 2 and two inequivalent irreducible Z＋-modules of rank 4 over K（Z3, 3）.
基金supported by National Natural Science Foundation of China (Grant Nos.10726014, 10801010)
文摘We construct a class of modules for extended affne Lie algebra ■ by using the free fields. A necessary and sufficient condition is given for those modules being irreducible.
基金Supported by the National Natural Science Foundation of China (Grant No.10671142)
文摘A monomial basis and a filtration of subalgebras for the universal enveloping algebra U（gl） of a complex simple Lie algebra gl of type Bl and Cl are given, and the decomposition of the Weyl module V （λ） as a U（gl）-module into a direct sum of Weyl modules V （μ）’s as U（gl-1）modules is described. In particular, a new multiplicity formula for the Weyl module V （λ） is obtained in this note.
基金Supported by the Nature Science Foundation of China(10671026)Natural Science Foundation of Heilongjiang Province(A201013)+1 种基金Postdoctoral Scientific Research Foundation of Heilongjiang Province(HB200801165)the fund of Heilongjiang Education Committee(11541268)
