For any complex parameters a, b, let W（a, b） be the Lie algebra with basis {Li, Hi｜i ∈ Z} and relations [Li,Lj] = （j - i）Li＋j, [Li,Hj] = （a ＋ j ＋ bi）Hi＋j and [Hi, Hi] = 0. In this paper, we construct the W...For any complex parameters a, b, let W（a, b） be the Lie algebra with basis {Li, Hi｜i ∈ Z} and relations [Li,Lj] = （j - i）Li＋j, [Li,Hj] = （a ＋ j ＋ bi）Hi＋j and [Hi, Hi] = 0. In this paper, we construct the W（a, b） conformal algebra for some a, b and its conformal module of rank one.展开更多
The first cohomology group of generalized loop Virasoro algebras with coefficients in the tensor product of its adjoint module is shown to be trivial. The result is used to prove that Lie bialgebra structures on gener...The first cohomology group of generalized loop Virasoro algebras with coefficients in the tensor product of its adjoint module is shown to be trivial. The result is used to prove that Lie bialgebra structures on generalized loop Virasoro algebras are coboundary triangular. The authors generalize the results to generalized map Virasoro algebras.展开更多
Let L be a Lie algebra of Block type over C with basis {Lα,i ｜ a,i ∈ Z} and brackets [Lα,i, Lβ,j] = （β（i ＋ 1） - α（j ＋ 1））Lα＋β,i＋j. In this paper, we first construct a formal distribution Lie algebra...Let L be a Lie algebra of Block type over C with basis {Lα,i ｜ a,i ∈ Z} and brackets [Lα,i, Lβ,j] = （β（i ＋ 1） - α（j ＋ 1））Lα＋β,i＋j. In this paper, we first construct a formal distribution Lie algebra of L. Then we decide its conformal algebra B with C[δ]- basis { Lα（w） ｜ α ∈ Z} and λ-brackets [Lα（w）λLβ（w）] = （αδ ＋ （α ＋β）A）Lα＋β（w）. Finally, we give a classification of free intermediate series B-modules.展开更多
In this paper,the structures of dual Lie bialgebras of twisted SchrSdinger-Virasoro type are investigated.By studying the maximal good subspaces,we determine the dual Lie coalgebras of the twisted SchrSdinger-Virasoro...In this paper,the structures of dual Lie bialgebras of twisted SchrSdinger-Virasoro type are investigated.By studying the maximal good subspaces,we determine the dual Lie coalgebras of the twisted SchrSdinger-Virasoro algebras.Then based on this,we construct the dual Lie bialgebra structures of this type.As by-products,four new infinite dimensional Lie algebras are obtained.展开更多
Let W(Г)be a class of not-finitely graded Lie algebras related to generalized Virasoro algebras with basis{L_(α,i),C|α∈Г,i∈Z_(+)},which satisfies relations[L_(α,i),L_(β,j)]=L_(α+β,i+j)+(j-i)L_(α+β,i+j+1)+...Let W(Г)be a class of not-finitely graded Lie algebras related to generalized Virasoro algebras with basis{L_(α,i),C|α∈Г,i∈Z_(+)},which satisfies relations[L_(α,i),L_(β,j)]=L_(α+β,i+j)+(j-i)L_(α+β,i+j+1)+δ_(α+β,0)δ_(i+j),0α^(3)-α/12 C and[C,L_(α,i)]=0.In this paper,W(Г)-modules of the intermediate series satisfying some conditions are constructed and classified.We also obtain modules of the intermediate series over the related Lie superalgebra.展开更多
文摘For any complex parameters a, b, let W（a, b） be the Lie algebra with basis {Li, Hi｜i ∈ Z} and relations [Li,Lj] = （j - i）Li＋j, [Li,Hj] = （a ＋ j ＋ bi）Hi＋j and [Hi, Hi] = 0. In this paper, we construct the W（a, b） conformal algebra for some a, b and its conformal module of rank one.
基金supported by the National Natural Science Foundation of China(Nos.10825101,11431010,11271284,11101269)the Scientific Research Starting Foundation for Doctors,Shanghai Ocean University(No.A-0209-13-0105380)the Youth Scholars of Shanghai Higher Education Institutions(No.ZZHY14026)
文摘The first cohomology group of generalized loop Virasoro algebras with coefficients in the tensor product of its adjoint module is shown to be trivial. The result is used to prove that Lie bialgebra structures on generalized loop Virasoro algebras are coboundary triangular. The authors generalize the results to generalized map Virasoro algebras.
文摘Let L be a Lie algebra of Block type over C with basis {Lα,i ｜ a,i ∈ Z} and brackets [Lα,i, Lβ,j] = （β（i ＋ 1） - α（j ＋ 1））Lα＋β,i＋j. In this paper, we first construct a formal distribution Lie algebra of L. Then we decide its conformal algebra B with C[δ]- basis { Lα（w） ｜ α ∈ Z} and λ-brackets [Lα（w）λLβ（w）] = （αδ ＋ （α ＋β）A）Lα＋β（w）. Finally, we give a classification of free intermediate series B-modules.
文摘In this paper,the structures of dual Lie bialgebras of twisted SchrSdinger-Virasoro type are investigated.By studying the maximal good subspaces,we determine the dual Lie coalgebras of the twisted SchrSdinger-Virasoro algebras.Then based on this,we construct the dual Lie bialgebra structures of this type.As by-products,four new infinite dimensional Lie algebras are obtained.
基金Supported by NSF grants 11431010 and 11971350 of China.
文摘Let W(Г)be a class of not-finitely graded Lie algebras related to generalized Virasoro algebras with basis{L_(α,i),C|α∈Г,i∈Z_(+)},which satisfies relations[L_(α,i),L_(β,j)]=L_(α+β,i+j)+(j-i)L_(α+β,i+j+1)+δ_(α+β,0)δ_(i+j),0α^(3)-α/12 C and[C,L_(α,i)]=0.In this paper,W(Г)-modules of the intermediate series satisfying some conditions are constructed and classified.We also obtain modules of the intermediate series over the related Lie superalgebra.
