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
Gel'fand-Dorfman bialgebra,which is both a Lie algebra and a Novikov algebra with some compatibility condition,appeared in the study of Hamiltonian pairs in completely integrable systems.They also emerged in the d...Gel'fand-Dorfman bialgebra,which is both a Lie algebra and a Novikov algebra with some compatibility condition,appeared in the study of Hamiltonian pairs in completely integrable systems.They also emerged in the description of a class special Lie conformal algebras called quadratic Lie conformal algebras.In this paper,we investigate the extending structures problem for Gel'fand-Dorfman bialgebras,which is equivalent to some extending structures problem of quadratic Lie conformal algebras.Explicitly,given a Gel'fand-Dorfman bialgebra(A,o,[.,.]),this problem is how to describe and classify all Gel'fand-Dorfman bialgebra structures on a vector space E(A⊂E)such that(A,o,[.,.])is a subalgebra of E up to an isomorphism whose restriction on A is the identity map.Motivated by the theories of extending structures for Lie algebras and Novikov algebras,we construct an object gH2(V,A)to answer the extending structures problem by introducing the notion of a unified product for Gel'fand-Dorfman bialgebras,where V is a complement of A in E.In particular,we investigate the special case when dim(V)=1 in detail.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
In this paper we classify the irreducible integrable modules for the core of the extended affine Lie algebra of type Ad-1 coordinated by Cq with finite-dimensional weight spaces and the center acting trivially, where ...In this paper we classify the irreducible integrable modules for the core of the extended affine Lie algebra of type Ad-1 coordinated by Cq with finite-dimensional weight spaces and the center acting trivially, where Cq is the quantum torus in two variables.展开更多
Let sv be the extended Schrödinger–Virasoro Lie algebra and n≥1 an integer.A map f:svn=sv×sv×⋯×sv→sv is called an n-derivation if it is a derivation in one variable while other variables fixed.W...Let sv be the extended Schrödinger–Virasoro Lie algebra and n≥1 an integer.A map f:svn=sv×sv×⋯×sv→sv is called an n-derivation if it is a derivation in one variable while other variables fixed.We investigate n-derivations of the extended Schrödinger–Virasoro Lie algebra sv.The main result when n=2 is then applied to characterize the linear commuting maps and the commutative post-Lie algebra structures on sv.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.
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
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
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
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 the National Natural Science Foundation of China(Grant Nos.12171129,11871421)the Zhejiang Provincial Natural Science Foundation of China(Grant No.LY20A010022)the Scientific Research Foundation of Hangzhou Normal University(Grant No.2019QDL012)。
文摘Gel'fand-Dorfman bialgebra,which is both a Lie algebra and a Novikov algebra with some compatibility condition,appeared in the study of Hamiltonian pairs in completely integrable systems.They also emerged in the description of a class special Lie conformal algebras called quadratic Lie conformal algebras.In this paper,we investigate the extending structures problem for Gel'fand-Dorfman bialgebras,which is equivalent to some extending structures problem of quadratic Lie conformal algebras.Explicitly,given a Gel'fand-Dorfman bialgebra(A,o,[.,.]),this problem is how to describe and classify all Gel'fand-Dorfman bialgebra structures on a vector space E(A⊂E)such that(A,o,[.,.])is a subalgebra of E up to an isomorphism whose restriction on A is the identity map.Motivated by the theories of extending structures for Lie algebras and Novikov algebras,we construct an object gH2(V,A)to answer the extending structures problem by introducing the notion of a unified product for Gel'fand-Dorfman bialgebras,where V is a complement of A in E.In particular,we investigate the special case when dim(V)=1 in detail.
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The third author was partially supported by NSF of China （10931006） and a grant from the PhD Programs Foundation of Ministry of Education of China （20100121110014）. The fourth author was partially supported by NSF of China （11371024）, Natural Science Foundation of Fujian Province （2013J01018） and Fundamental Research Funds for the Central University （2013121001）.
文摘In this paper we classify the irreducible integrable modules for the core of the extended affine Lie algebra of type Ad-1 coordinated by Cq with finite-dimensional weight spaces and the center acting trivially, where Cq is the quantum torus in two variables.
基金This work was supported in part by the NSFC(No.11771069)the NSF of Heilongjiang Province(No.LH2020A020)the Fund of Heilongjiang Provincial Laboratory of the Theory and Computation of Complex Systems。
文摘Let sv be the extended Schrödinger–Virasoro Lie algebra and n≥1 an integer.A map f:svn=sv×sv×⋯×sv→sv is called an n-derivation if it is a derivation in one variable while other variables fixed.We investigate n-derivations of the extended Schrödinger–Virasoro Lie algebra sv.The main result when n=2 is then applied to characterize the linear commuting maps and the commutative post-Lie algebra structures on sv.
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 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.
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 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.
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.
