The twisted Heisenberg-Virasoro algebra is the universal central extension of the Lie algebra of differential operators on a circle of order at most one.In this paper,we first study the variety of semi-conformal vecto...The twisted Heisenberg-Virasoro algebra is the universal central extension of the Lie algebra of differential operators on a circle of order at most one.In this paper,we first study the variety of semi-conformal vectors of the twisted Heisenberg-Virasoro vertex operator algebra,which is a finite set consisting of two nontrivial elements.Based on this property,we also show that the twisted Heisenberg-Virasoro vertex operator algebra is a tensor product of two vertex operator algebras.Moreover,associating to properties of semi-conformal vectors of the twisted Heisenberg-Virasoro vertex operator algebra,we charaterized twisted Heisenberg-Virasoro vertex operator algebras.This will be used to understand the classification problems of vertex operator algebras whose varieties of semi-conformal vectors are finite sets.展开更多
We show that the support of an irreducible weight module over the twisted Heisenberg-Virasoro algebra, which has an infinite-dimensional weight space, coincides with the weight lattice and that all nontrivial weight s...We show that the support of an irreducible weight module over the twisted Heisenberg-Virasoro algebra, which has an infinite-dimensional weight space, coincides with the weight lattice and that all nontrivial weight spaces of such a module are infinite dimensional. As a corollary, we obtain that every irreducible weight module over the twisted Heisenber-Virasoro algebra, having a nontrivial finite-dimensional weight space, is a Harish-Chandra module （and hence is either an irreducible highest or lowest weight module or an irreducible module from the intermediate series）.展开更多
The compatible left-symmetric algebra structures on the twisted Heisenberg-Virasoro algebra with some natural grading conditions are completely determined. The results of the earlier work on left-symmetric algebra str...The compatible left-symmetric algebra structures on the twisted Heisenberg-Virasoro algebra with some natural grading conditions are completely determined. The results of the earlier work on left-symmetric algebra structures on the Virasoro algebra play an essential role in determining these compatible structures. As a corollary, any such left-symmetric algebra contains an infinite-dimensional nontrivial subalgebra that is also a submodu]e of the regular module.展开更多
Let DN be the multicomponent twisted Heisenberg-Virasoro algebra.We compute the second continuous cohomology group with cofficients in C and study the biharmiltonian Euler equations associated to DN and its central ex...Let DN be the multicomponent twisted Heisenberg-Virasoro algebra.We compute the second continuous cohomology group with cofficients in C and study the biharmiltonian Euler equations associated to DN and its central extensions.展开更多
The conjugate-linear anti-involutions and unitary irreducible modules of the intermediate series over the twisted Heisenberg-Virasoro algebra are classified,respectively.We prove that any unitary irreducible module of...The conjugate-linear anti-involutions and unitary irreducible modules of the intermediate series over the twisted Heisenberg-Virasoro algebra are classified,respectively.We prove that any unitary irreducible module of the intermediate series over the twisted Heisenberg-Virasoro algebra is of the form Aa,b,c for a ∈ R,6∈1/2+√-1R and c∈C.展开更多
In this paper, we mainly determine the compatible left-symmetric algebra structures on the planar Galilean conformal algebra with some natural grading conditions. The results of earlier work on left-symmetric algebra ...In this paper, we mainly determine the compatible left-symmetric algebra structures on the planar Galilean conformal algebra with some natural grading conditions. The results of earlier work on left-symmetric algebra structures on the twisted Heisenberg-Virasoro algebra play an important role in determining these compatible structures. As a corollary, any such left-symmetric algebra contains an infinite-dimensional non-trivial subalgebra that is also a submodule of the regular module.展开更多
基金supported by The Key Research Project of Institutions of Higher Education in Henan Province,P.R.China(No.17A11003)
文摘The twisted Heisenberg-Virasoro algebra is the universal central extension of the Lie algebra of differential operators on a circle of order at most one.In this paper,we first study the variety of semi-conformal vectors of the twisted Heisenberg-Virasoro vertex operator algebra,which is a finite set consisting of two nontrivial elements.Based on this property,we also show that the twisted Heisenberg-Virasoro vertex operator algebra is a tensor product of two vertex operator algebras.Moreover,associating to properties of semi-conformal vectors of the twisted Heisenberg-Virasoro vertex operator algebra,we charaterized twisted Heisenberg-Virasoro vertex operator algebras.This will be used to understand the classification problems of vertex operator algebras whose varieties of semi-conformal vectors are finite sets.
基金NSF Grants 10471096,10571120 of China"One Hundred Talents Program"from the University of Science and Technology of China
文摘We show that the support of an irreducible weight module over the twisted Heisenberg-Virasoro algebra, which has an infinite-dimensional weight space, coincides with the weight lattice and that all nontrivial weight spaces of such a module are infinite dimensional. As a corollary, we obtain that every irreducible weight module over the twisted Heisenber-Virasoro algebra, having a nontrivial finite-dimensional weight space, is a Harish-Chandra module （and hence is either an irreducible highest or lowest weight module or an irreducible module from the intermediate series）.
基金supported by Postdoctoral Science Foundation of China(Grant No.201003326)National Natural Science Foundation of China(Grant Nos.11101056 and 11271056)
文摘The compatible left-symmetric algebra structures on the twisted Heisenberg-Virasoro algebra with some natural grading conditions are completely determined. The results of the earlier work on left-symmetric algebra structures on the Virasoro algebra play an essential role in determining these compatible structures. As a corollary, any such left-symmetric algebra contains an infinite-dimensional nontrivial subalgebra that is also a submodu]e of the regular module.
基金supported in part by the National Natural Science Foundation of China(Grant Nos.12071451,11671371,11871446).
文摘Let DN be the multicomponent twisted Heisenberg-Virasoro algebra.We compute the second continuous cohomology group with cofficients in C and study the biharmiltonian Euler equations associated to DN and its central extensions.
基金Supported by the National Natural Science Foundation of China(Nos.11571145,11531004,11471333 and 11471268).
文摘The conjugate-linear anti-involutions and unitary irreducible modules of the intermediate series over the twisted Heisenberg-Virasoro algebra are classified,respectively.We prove that any unitary irreducible module of the intermediate series over the twisted Heisenberg-Virasoro algebra is of the form Aa,b,c for a ∈ R,6∈1/2+√-1R and c∈C.
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)
文摘In this paper, we mainly determine the compatible left-symmetric algebra structures on the planar Galilean conformal algebra with some natural grading conditions. The results of earlier work on left-symmetric algebra structures on the twisted Heisenberg-Virasoro algebra play an important role in determining these compatible structures. As a corollary, any such left-symmetric algebra contains an infinite-dimensional non-trivial subalgebra that is also a submodule of the regular module.
