We classify modules which are free of rank 1 when restricted to the negative part for the Euclidean Lie algebra.Sufficient and necessary conditions for the simplicity of these modules are given.From these modules we c...We classify modules which are free of rank 1 when restricted to the negative part for the Euclidean Lie algebra.Sufficient and necessary conditions for the simplicity of these modules are given.From these modules we construct modules which are infinitely generated when restricted to the maximal toral subalgebra.展开更多
Over an algebraically closed field of characteristic p>2,based on the results on the representation theory of special linear Lie algebra sl(2),restricted simple modules L(λ)of the Schrodinger algebra S(1)are deter...Over an algebraically closed field of characteristic p>2,based on the results on the representation theory of special linear Lie algebra sl(2),restricted simple modules L(λ)of the Schrodinger algebra S(1)are determined,and all derivations of S(1)on L(λ)are also obtained.As an application,the first cohomology of S(1)with the coefficient in L(λ)is determined.展开更多
The coordinate ring O_(q)(K^(n))of quantum affine space is the K-algebra presented by generators x_(1),...,x_(n) and relations x_(i)x_(j)=q_(ij)a_(j)a_(i) for all i,j.We construct simple O_(q)(K^(n))-modules in a more...The coordinate ring O_(q)(K^(n))of quantum affine space is the K-algebra presented by generators x_(1),...,x_(n) and relations x_(i)x_(j)=q_(ij)a_(j)a_(i) for all i,j.We construct simple O_(q)(K^(n))-modules in a more general setting where the parameters qij lie in a torsion subgroup of K^(*)and show that analogous results hold as in the uniparameter case.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
Let n be a natural number, and let A be an indecomposable cellular algebra such that the spectrum of its Cartan matrix C is of theform {n, 1,..., 1}. In general, not every natural number could be the number of non-iso...Let n be a natural number, and let A be an indecomposable cellular algebra such that the spectrum of its Cartan matrix C is of theform {n, 1,..., 1}. In general, not every natural number could be the number of non-isomorphic simple modules over such a cellular algebra. Thus, two natural questions arise: (1) which numbers could be the number of non-isomorphic simple modules over such a cellular algebra A ? (2) Given such a number, is there a cellular algebra such that its Cartan matrix has the desired property ? In this paper, we shall completely answer the first question, and give a partial answer to the second question by constructing cellular algebras with the pre-described Cartan matrix.展开更多
基金supported by NSF of China(11801117,11971315)the Natural Science Foundation of Guangdong Province,China(2018A030313268)partially supported by NSFof China(11801390).
文摘We classify modules which are free of rank 1 when restricted to the negative part for the Euclidean Lie algebra.Sufficient and necessary conditions for the simplicity of these modules are given.From these modules we construct modules which are infinitely generated when restricted to the maximal toral subalgebra.
文摘Over an algebraically closed field of characteristic p>2,based on the results on the representation theory of special linear Lie algebra sl(2),restricted simple modules L(λ)of the Schrodinger algebra S(1)are determined,and all derivations of S(1)on L(λ)are also obtained.As an application,the first cohomology of S(1)with the coefficient in L(λ)is determined.
文摘The coordinate ring O_(q)(K^(n))of quantum affine space is the K-algebra presented by generators x_(1),...,x_(n) and relations x_(i)x_(j)=q_(ij)a_(j)a_(i) for all i,j.We construct simple O_(q)(K^(n))-modules in a more general setting where the parameters qij lie in a torsion subgroup of K^(*)and show that analogous results hold as in the uniparameter case.
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This research work was supported by CFKSTIP(Grant No.704004)the Doctor Program Foundation(Grant No.20040027002),Ministry of Education of Chinapartially by National Natural Science Foundation of China(Grant No.103331030).
文摘Let n be a natural number, and let A be an indecomposable cellular algebra such that the spectrum of its Cartan matrix C is of theform {n, 1,..., 1}. In general, not every natural number could be the number of non-isomorphic simple modules over such a cellular algebra. Thus, two natural questions arise: (1) which numbers could be the number of non-isomorphic simple modules over such a cellular algebra A ? (2) Given such a number, is there a cellular algebra such that its Cartan matrix has the desired property ? In this paper, we shall completely answer the first question, and give a partial answer to the second question by constructing cellular algebras with the pre-described Cartan matrix.
