In this paper, the extended affine Lie algebra sl2（Cq） is quantized from three different points of view, which produces three non-commutative and non-cocommutative Hopf algebra structures, and yields other three qua...In this paper, the extended affine Lie algebra sl2（Cq） is quantized from three different points of view, which produces three non-commutative and non-cocommutative Hopf algebra structures, and yields other three quantizations by an isomorphism of sl2 （Cq） correspondingly. Moreover, two of these quantizations can be restricted to the extended affine Lie algebra sl2（Cq）.展开更多
Non-commutative Poisson algebras are the algebras having both an associa- tive algebra structure and a Lie algebra structure together with the Leibniz law. In this paper, the non-commutative poisson algebra structures...Non-commutative Poisson algebras are the algebras having both an associa- tive algebra structure and a Lie algebra structure together with the Leibniz law. In this paper, the non-commutative poisson algebra structures on the Lie algebras sln（Cq^-） are determined.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.
Let g be a(twisted or untwisted)affine Kac-Moody algebra,and μ be a diagram automorphism of g.In this paper,we give an explicit realization for the universal central extensionˆg[μ]of the twisted loop algebra of g wi...Let g be a(twisted or untwisted)affine Kac-Moody algebra,and μ be a diagram automorphism of g.In this paper,we give an explicit realization for the universal central extensionˆg[μ]of the twisted loop algebra of g with respect toμ,which provides a Moody-Rao-Yokonuma presentation for the algebraˆg[μ]whenμis non-transitive,and the presentation is indeed related to the quantization of twisted toroidal Lie algebras.展开更多
In this paper, we give explicit realizations for the irreducible integrable modules, which were clas- sified in Chang and Tan [Pacific J Math, 2011, 252: 293-312], of the extended baby TKK algebra. Moreover, condition...In this paper, we give explicit realizations for the irreducible integrable modules, which were clas- sified in Chang and Tan [Pacific J Math, 2011, 252: 293-312], of the extended baby TKK algebra. Moreover, conditions for these modules to be unitary are determined.展开更多
We find a class of Lie algebras, which are defined from the symmetrizable generalized intersection matrices. However, such algebras are different from generalized intersection matrix algebras and intersection matrix a...We find a class of Lie algebras, which are defined from the symmetrizable generalized intersection matrices. However, such algebras are different from generalized intersection matrix algebras and intersection matrix algebras. Moreover, such Lie algebras generated by semi-positive definite matrices can be classified by the modified Dynkin diagrams.展开更多
文摘In this paper, the extended affine Lie algebra sl2（Cq） is quantized from three different points of view, which produces three non-commutative and non-cocommutative Hopf algebra structures, and yields other three quantizations by an isomorphism of sl2 （Cq） correspondingly. Moreover, two of these quantizations can be restricted to the extended affine Lie algebra sl2（Cq）.
基金supported by NSF of China(11071187)Innovation Program of Shanghai Municipal Education Commission(09YZ336)
文摘Non-commutative Poisson algebras are the algebras having both an associa- tive algebra structure and a Lie algebra structure together with the Leibniz law. In this paper, the non-commutative poisson algebra structures on the Lie algebras sln（Cq^-） are determined.
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supported by National Natural Science Foundation of China(Grant Nos.11531004 and 11701183)the Fundamental Research Funds for the Central Universities(Grant No.20720190069)the Simons Foundation(Grant No.198129)。
文摘Let g be a(twisted or untwisted)affine Kac-Moody algebra,and μ be a diagram automorphism of g.In this paper,we give an explicit realization for the universal central extensionˆg[μ]of the twisted loop algebra of g with respect toμ,which provides a Moody-Rao-Yokonuma presentation for the algebraˆg[μ]whenμis non-transitive,and the presentation is indeed related to the quantization of twisted toroidal Lie algebras.
基金supported by National Natural Science Foundation of China (Grant No.10931006)the PhD Programs Foundation of Ministry of Education of China (Grant No. 20100121110014)
文摘In this paper, we give explicit realizations for the irreducible integrable modules, which were clas- sified in Chang and Tan [Pacific J Math, 2011, 252: 293-312], of the extended baby TKK algebra. Moreover, conditions for these modules to be unitary are determined.
文摘We find a class of Lie algebras, which are defined from the symmetrizable generalized intersection matrices. However, such algebras are different from generalized intersection matrix algebras and intersection matrix algebras. Moreover, such Lie algebras generated by semi-positive definite matrices can be classified by the modified Dynkin diagrams.
