It is known that the Schrddinger-Virasoro algebras, including the original Schrddinger-Virasoro algebra and the twisted Schr?dinger-Virasoro algebra, are playing important roles in mathematics and statistical physics....It is known that the Schrddinger-Virasoro algebras, including the original Schrddinger-Virasoro algebra and the twisted Schr?dinger-Virasoro algebra, are playing important roles in mathematics and statistical physics. In this paper, we study the tensor products of weight modules over the Schr?dinger- Virasoro algebras. The irreducibility criterion for the tensor products of highest weight modules with intermediate series modules over the Schr?dinger-Virasoro algebra is obtained.展开更多
It is shown that the support of an irreducible weight module over the SchrSdinger-Virasoro Lie algebra with an infinite-dimensional weight space coincides with the weight lattice, and all nontrivial weight spaces of s...It is shown that the support of an irreducible weight module over the SchrSdinger-Virasoro Lie algebra with an infinite-dimensional weight space coincides with the weight lattice, and all nontrivial weight spaces of such a module are infinite-dimensional. As a by-product, it is obtained that every simple weight module over Lie algebra of this type with a nontrivial finite-dimensional weight space is a Harish-Chandra module.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
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
We give a classification of Lie bialgebra structures on generalized loop Schr?dinger-Virasoro algebras st). Then we find out that not all Lie bialgebra structures on generalized loop Schr?dinger-Virasoro algebras st) ...We give a classification of Lie bialgebra structures on generalized loop Schr?dinger-Virasoro algebras st). Then we find out that not all Lie bialgebra structures on generalized loop Schr?dinger-Virasoro algebras st) are triangular coboundary.展开更多
基金the National Natural Science Foundation of China(Grant Nos.11571145,11871249)the Natural Science Foundation of Zhejiang Province(No.LZ14A010001).
文摘It is known that the Schrddinger-Virasoro algebras, including the original Schrddinger-Virasoro algebra and the twisted Schr?dinger-Virasoro algebra, are playing important roles in mathematics and statistical physics. In this paper, we study the tensor products of weight modules over the Schr?dinger- Virasoro algebras. The irreducibility criterion for the tensor products of highest weight modules with intermediate series modules over the Schr?dinger-Virasoro algebra is obtained.
基金Supported by National Natural Science Foundation of China(11971315,11871249)Scientific Research Project of Huzhou University(The structures and representations of several types of infinite dimensional Lie algebras)
基金Supported by National Natural Science Foundation of China(11201141,11371134)Natural Science Foundation of Zhejiang Province(LQ12A01005,LZ14A010001)Project of Huzhou University(KX21059,2014XJKY50)
基金Supported by China Postdoctoral Science Foundation Grant 20080440720, NSF Grants 10671027, 10825101 of China and ＂One Hundred Talents Program＂ from University of Science and Technology of China
文摘It is shown that the support of an irreducible weight module over the SchrSdinger-Virasoro Lie algebra with an infinite-dimensional weight space coincides with the weight lattice, and all nontrivial weight spaces of such a module are infinite-dimensional. As a by-product, it is obtained that every simple weight module over Lie algebra of this type with a nontrivial finite-dimensional weight space is a Harish-Chandra module.
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.
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the National Natural Science Foundation of China(Grant Nos.11801369,11771279,11801363,11431010)the Natural Science Foundation of Shanghai(Grant No.16ZR1415000).
文摘We give a classification of Lie bialgebra structures on generalized loop Schr?dinger-Virasoro algebras st). Then we find out that not all Lie bialgebra structures on generalized loop Schr?dinger-Virasoro algebras st) are triangular coboundary.
