We find an exact formula of Gelfand-Kirillov dimensions for the infinite-dimensional explicit irreducible sl（n,F）-modules that appeared in the Z2-graded oscillator generalizations of the classical theorem on harmoni...We find an exact formula of Gelfand-Kirillov dimensions for the infinite-dimensional explicit irreducible sl（n,F）-modules that appeared in the Z2-graded oscillator generalizations of the classical theorem on harmonic polynomials established by Luo and Xu. Three infinite subfamilies of these modules have the minimal Gelfand-Kirillov dimension. They contain weight modules with unbounded weight multiplicities and completely pointed modules.Service E-mail this articleAdd to my bookshelfAdd to citation managerE-mail AlertRSSArticles by authors展开更多
Let F be an algebraically closed field and charF=0. In this note, using the method ofmixed product in ref. [1], the irreducible positive （negative） Z-graded module of Liesuperalgebra H（n） with base space V （top s...Let F be an algebraically closed field and charF=0. In this note, using the method ofmixed product in ref. [1], the irreducible positive （negative） Z-graded module of Liesuperalgebra H（n） with base space V （top space V） is determined, where the highest weightof H（n）<sub>0</sub>-module V is not kλ<sub>1</sub> for any nonnegative integer k.展开更多
Let y be a generalized Kac-Moody algebra with an integral Borcherds-Cartan matrix. In this paper, we define a d-type weak quantum generalized Kac-Moody algebra wUq^d（y）, which is a weak Hopf algebra. We also study t...Let y be a generalized Kac-Moody algebra with an integral Borcherds-Cartan matrix. In this paper, we define a d-type weak quantum generalized Kac-Moody algebra wUq^d（y）, which is a weak Hopf algebra. We also study the highest weight module over the weak quantum algebra wUdq^d（y） and weak A-forms of wUq^d（y）.展开更多
We investigate the highest weight representations of the q-deformed Virasoro algebra of Hom-type. In order to determine its unitarity and irreducible highest weight representations, we present its Kac determinant form...We investigate the highest weight representations of the q-deformed Virasoro algebra of Hom-type. In order to determine its unitarity and irreducible highest weight representations, we present its Kac determinant formula when q is nonzero and non-root of unity.展开更多
The aim of this paper is to study the adjoint action for the quantum algebra Uq（f（K, H））, which is a natural generalization of quantum algebra Uq（sl2） and is regarded as a class of generalized Weyl algebra..The ...The aim of this paper is to study the adjoint action for the quantum algebra Uq（f（K, H））, which is a natural generalization of quantum algebra Uq（sl2） and is regarded as a class of generalized Weyl algebra..The structure theorem of its locally finite subalgebra F（Uq（f（K, H））） is given.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
In refs. [1—3] level one highest weight representations of complete infinite rank affine Lie algebra A_∞ were discussed. Since C_∞ is a subalgebra of A_∞, any representation of A_∞ induces a representation of C_...In refs. [1—3] level one highest weight representations of complete infinite rank affine Lie algebra A_∞ were discussed. Since C_∞ is a subalgebra of A_∞, any representation of A_∞ induces a representation of C_∞. In this note, we discuss the relations of irreducible highest weight representations of A_∞ and C_∞.展开更多
Borcherds introduced the so-called generalized Kac-Moody algebras (GKM alge-bras for short), whose outstanding characteristic is the emergence of the imaginarysimple roots. This note investigates some properties of in...Borcherds introduced the so-called generalized Kac-Moody algebras (GKM alge-bras for short), whose outstanding characteristic is the emergence of the imaginarysimple roots. This note investigates some properties of integrable highest weightmodules for GKM algebras.展开更多
基金Supported by National Natural Science Foundation of China(Grant No.11171324)
文摘We find an exact formula of Gelfand-Kirillov dimensions for the infinite-dimensional explicit irreducible sl（n,F）-modules that appeared in the Z2-graded oscillator generalizations of the classical theorem on harmonic polynomials established by Luo and Xu. Three infinite subfamilies of these modules have the minimal Gelfand-Kirillov dimension. They contain weight modules with unbounded weight multiplicities and completely pointed modules.Service E-mail this articleAdd to my bookshelfAdd to citation managerE-mail AlertRSSArticles by authors
基金Project supported by the National Natural Science Foundation of China.
文摘Let F be an algebraically closed field and charF=0. In this note, using the method ofmixed product in ref. [1], the irreducible positive （negative） Z-graded module of Liesuperalgebra H（n） with base space V （top space V） is determined, where the highest weightof H（n）<sub>0</sub>-module V is not kλ<sub>1</sub> for any nonnegative integer k.
基金Supported in part by the Scientific Research Foundation of Zhejiang Provincial Education Department under grant number 20040322It is also sponsored by SRF for ROCS,SEM
文摘Let y be a generalized Kac-Moody algebra with an integral Borcherds-Cartan matrix. In this paper, we define a d-type weak quantum generalized Kac-Moody algebra wUq^d（y）, which is a weak Hopf algebra. We also study the highest weight module over the weak quantum algebra wUdq^d（y） and weak A-forms of wUq^d（y）.
基金Supported by the National Natural Science Foundation of China(11047030)Supported by the Science and Technology Program of Henan Province(152300410061)
文摘We investigate the highest weight representations of the q-deformed Virasoro algebra of Hom-type. In order to determine its unitarity and irreducible highest weight representations, we present its Kac determinant formula when q is nonzero and non-root of unity.
基金Foundation item： the National Natural Science Foundation of China （No. 10871227） the Science Foundation of Hebei Province （No. 2008000135）.
文摘The aim of this paper is to study the adjoint action for the quantum algebra Uq（f（K, H））, which is a natural generalization of quantum algebra Uq（sl2） and is regarded as a class of generalized Weyl algebra..The structure theorem of its locally finite subalgebra F（Uq（f（K, H））） is given.
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.
文摘In refs. [1—3] level one highest weight representations of complete infinite rank affine Lie algebra A_∞ were discussed. Since C_∞ is a subalgebra of A_∞, any representation of A_∞ induces a representation of C_∞. In this note, we discuss the relations of irreducible highest weight representations of A_∞ and C_∞.
基金Hebei Province Science Foundation Grant, No 193005
文摘Borcherds introduced the so-called generalized Kac-Moody algebras (GKM alge-bras for short), whose outstanding characteristic is the emergence of the imaginarysimple roots. This note investigates some properties of integrable highest weightmodules for GKM algebras.
