In this paper, we discuss the pairing problem of generators in four affine Lie algebra. That is, for any given imaginary root vector x∈g(A) , there exists y such that x and y generate a subalgebra cont...In this paper, we discuss the pairing problem of generators in four affine Lie algebra. That is, for any given imaginary root vector x∈g(A) , there exists y such that x and y generate a subalgebra containing g′(A).展开更多
For any finite-dimensional semisimple Lie algebra g,a Z_+-graded vertex algebra is construsted on thevacuum representation V_k([θ]) of [θ],which is a one-dimentional central extension of θ-invariant subspace on the...For any finite-dimensional semisimple Lie algebra g,a Z_+-graded vertex algebra is construsted on thevacuum representation V_k([θ]) of [θ],which is a one-dimentional central extension of θ-invariant subspace on the loopalgebra Lg=gC((t~^(1/P))).展开更多
In this paper, the representation theory for the arlene Lie algebra H4 associated to the Nappi-Witten Lie algebra H4 is studied. Polynomial representations of the affine Nappi-Witten Lie algebra H4 are given.
The Nappi-Witten Lie algebra was first introduced by C. Nappi and E. Witten in the study of Wess-Zumino-Novikov-Witten (WZNW) models. They showed that the WZNW model (NW model) based on a central extension of the two-...The Nappi-Witten Lie algebra was first introduced by C. Nappi and E. Witten in the study of Wess-Zumino-Novikov-Witten (WZNW) models. They showed that the WZNW model (NW model) based on a central extension of the two-dimensional Euclidean group describes the homogeneous four-dimensional space-time corresponding to a gravitational plane wave. The associated Lie algebra is neither abelian nor semisimple. Recently K. Christodoulopoulou studied the irreducible Whittaker modules for finite- and infinite-dimensional Heisenberg algebras and for the Lie algebra obtained by adjoining a degree derivation to an infinite-dimensional Heisenberg algebra, and used these modules to construct a new class of modules for non-twisted affine algebras, which are called imaginary Whittaker modules. In this paper, imaginary Whittaker modules of the twisted affine Nappi-Witten Lie algebra are constructed based on Whittaker modules of Heisenberg algebras. It is proved that the imaginary Whittaker module with the center acting as a non-zero scalar is irreducible.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
Some properties of automorphisms of affine Lie algebras are presented. Automorphisms with order three are classified up to conjugacy, and their fixed point sets are also computed. As a corollary, it is proved that two...Some properties of automorphisms of affine Lie algebras are presented. Automorphisms with order three are classified up to conjugacy, and their fixed point sets are also computed. As a corollary, it is proved that two automorphisms of order three are conjugate if and only if their fixed point sets are isomorphic.展开更多
The purpose of this paper is to construct quotient algebras L(A)1C/I(A) of complex degenerate composition Lie algebras L(A)1C by some ideals, where L(A)1C is defined via Hall algebras of tubular algebras A, and to pro...The purpose of this paper is to construct quotient algebras L(A)1C/I(A) of complex degenerate composition Lie algebras L(A)1C by some ideals, where L(A)1C is defined via Hall algebras of tubular algebras A, and to prove that the quotient algebras L(A)1C/I(A) are isomorphic to the corresponding affine Kac-Moody algebras. Moreover, it is shown that the Lie algebra Lre(A)1C generated by A-modules with a real root coincides with the degenerate composition Lie algebra L(A)1C generated by simple A-modules.展开更多
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
An explicit construction of irreducible representations for the affine-Virasoro Lie algebra of type Bl, through the use of vertex operators and certain oscillator representations of the Virasoro algebra, is given.
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
文摘In this paper, we discuss the pairing problem of generators in four affine Lie algebra. That is, for any given imaginary root vector x∈g(A) , there exists y such that x and y generate a subalgebra containing g′(A).
基金National Key Basic Research Project of China under Grant Nos.2004CB318000 and 2006CB805905National Natural Science Foundation of China under Grant No.10471034+1 种基金the Outstanding Youth Fund of Henan Province under Grant No.0512000100Innovation Fund of Colleges and Universities in Henan Province
文摘For any finite-dimensional semisimple Lie algebra g,a Z_+-graded vertex algebra is construsted on thevacuum representation V_k([θ]) of [θ],which is a one-dimentional central extension of θ-invariant subspace on the loopalgebra Lg=gC((t~^(1/P))).
基金Supported in part by NSFC(10871125,10931006)a grant of Science and Technology Commission of Shanghai Municipality(09XD1402500)
文摘In this paper, the representation theory for the arlene Lie algebra H4 associated to the Nappi-Witten Lie algebra H4 is studied. Polynomial representations of the affine Nappi-Witten Lie algebra H4 are given.
基金Supported in part by National Natural Science Foundation of China under Grant No. 10971071the Outstanding Youth Fund of Henan Province under Grant No. 0512000100Innovation Fund of Colleges and Universities in Henan Province
文摘In this paper, we construct a new algebra structure 7-twisted affine Lie algebra ■[θ] and study itsvertex operator representations.
文摘The Nappi-Witten Lie algebra was first introduced by C. Nappi and E. Witten in the study of Wess-Zumino-Novikov-Witten (WZNW) models. They showed that the WZNW model (NW model) based on a central extension of the two-dimensional Euclidean group describes the homogeneous four-dimensional space-time corresponding to a gravitational plane wave. The associated Lie algebra is neither abelian nor semisimple. Recently K. Christodoulopoulou studied the irreducible Whittaker modules for finite- and infinite-dimensional Heisenberg algebras and for the Lie algebra obtained by adjoining a degree derivation to an infinite-dimensional Heisenberg algebra, and used these modules to construct a new class of modules for non-twisted affine algebras, which are called imaginary Whittaker modules. In this paper, imaginary Whittaker modules of the twisted affine Nappi-Witten Lie algebra are constructed based on Whittaker modules of Heisenberg algebras. It is proved that the imaginary Whittaker module with the center acting as a non-zero scalar is irreducible.
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Some properties of automorphisms of affine Lie algebras are presented. Automorphisms with order three are classified up to conjugacy, and their fixed point sets are also computed. As a corollary, it is proved that two automorphisms of order three are conjugate if and only if their fixed point sets are isomorphic.
基金supported in part by the National Natural Science Foundation of China(Grant No.10471034)Famous Youth Foundation of Henan Province(Grant No.0512000100)the Natural Science Foundation of Educational Committee of Henan Province(Grant No.2000110010).
文摘In this paper, we define a P-twisted affine Lie algebra, and construct its realizations by twisted vertex operators.
基金Supported by the National Natural Science Foundation of China (Grant Nos. 10371101 and 10671161)
文摘The purpose of this paper is to construct quotient algebras L(A)1C/I(A) of complex degenerate composition Lie algebras L(A)1C by some ideals, where L(A)1C is defined via Hall algebras of tubular algebras A, and to prove that the quotient algebras L(A)1C/I(A) are isomorphic to the corresponding affine Kac-Moody algebras. Moreover, it is shown that the Lie algebra Lre(A)1C generated by A-modules with a real root coincides with the degenerate composition Lie algebra L(A)1C generated by simple A-modules.
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Project supported by the National Natural Science Foundation of China (No.10271076, No.10171023)
文摘An explicit construction of irreducible representations for the affine-Virasoro Lie algebra of type Bl, through the use of vertex operators and certain oscillator representations of the Virasoro algebra, is given.
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.
