Junbo Li, Yucai Su
In this paper it is proved that an irreducible weight module with finite-dimensional weight spaces over the Schrödinger-Virasoro algebras is a highest/lowest weight module or a uniformly bounded module. Furthermore, indecomposable modules of the intermediate series over these algebras are completely determined.
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In this paper, we determine the derivation algebra and the automorphism group of the original deformative ${\rm Schr\ddot{o}dinger}$-{\rm Virasoro} algebras which is the semi-direct product Lie algebra of the Witt algebra and its tensor density module ${\rm I^g}(a,b)$.
Local derivation on the $n$-th Schr{ö}dinger algebra
本文研究第n个薛定谔代数上的局部导子，证明了其上的每个局部导子都是导子。
Local derivation on the Schr{ö}dinger Lie algebra in $(n+1)$-dimensional space-time
本文研究了$(n+1)$维时空中Schr{ö}dinger李代数$\ms_n$的局部导子，并证明其上的每个局部导子均为导子。
Transposed Poisson structures on the extended Schrödinger-Virasoro and the original deformative Schrödinger-Virasoro algebras
本文计算了扩展与原始形变Schrödinger-Virasoro代数的1/2-导子，证明前者无非平凡1/2-导子及转置Poisson结构，而后者具有非平凡1/2-导子从而存在非平凡转置Poisson结构。
In this paper, conjugate-linear anti-involutions and unitary Harish-Chandra modules over the Schrödinger-Virasoro algebra are studied. It is proved that there are only two classes conjugate-linear anti-involutions over the Schrödinger-Virasoro algebra. The main result of this paper is that a unitary Harish-Chandra module over the Schrödinger-Virasoro algebra is simply a unitary Harish-Chandra module over the Virasoro algebra.
In a series of papers by Henkel, Roger and Unterberger, Schrödinger-Virasoro algebras and their deformations were introduced and investigated. In the present paper we determine the 2-cocycles of a class of deformative Schrödinger-Virasoro algebras.
In this paper, we investigate the skew-symmertric biderivations of the deformative Schrodinger-Virasoro Lie algebras which contain the twisted and original deformative Schrodinger-Virasoro Lie algebras. As an application, we give the explicit form of each linear commuting map on the deformative Schrodinger-Virasoro Lie algebras. In particular, we obtain that there exist non-inner biderivations and non-standard linear commuting maps for the certain deformative Schrodinger-Virasoro Lie algebras.
Both original and twisted Schrödinger-Virasoro algebras also their deformations were introduced and investigated in a series of papers by Henkel, Roger and Unterberger. In the present paper we aim to determine the 2-cocycles of original deformative Schrödinger-Virasoro algebras.
Both the basic cohomology groups and the reduced cohomology groups of the Schrödinger-Virasoro conformal algebra with trivial coefficients are completely determined.
In this article, we determine the derivation algebra and the automorphism group of the twisted Schrödinger-Virasoro algebra.
In this paper we investigate Lie bialgebra structures on the Schrödinger-Virasoro algebra $\LL$. Surprisingly, we find out an interesting fact that not all Lie bialgebra structures on the Schrödinger-Virasoro algebra are triangular coboundary, which is different from the related known results of some Lie algebras related to the Virasoro algebra.
In this paper, we study extensions between two finite irreducible conformal modules over the Schrödinger-Virasoro conformal algebra and the extended Schrödinger-Virasoro conformal algebra. Also, we classify all finite nontrivial irreducible conformal modules over the extended Schrödinger-Virasoro conformal algebra. As a byproduct, we obtain a classification of extensions of Heisenberg-Virasoro conformal modules.
In this paper we present all the Leibniz 2-cocycles of the twisted Schrödinger-Virasoro algebra, which determine its second Leibniz cohomology group.
In the present paper we shall determine all the non-degenerate symmetric invariant bilinear forms on the deformative Schrödinger-Virasoro algebras.
In this paper, we characterize the biderivations of Schrödinger-Virasoro Lie algebra. We get a classes of non-inner and non-skewsymmetric biderivations. As application, we characterize the commutative post-Lie algebra structures on Schrödinger-Virasoro Lie algebra.
In this paper the derivation algebra and automorphism group of the twisted deformative Schrödinger-Virasoro Lie algebras are determined.
In this paper we investigate Lie bialgebra structures on the deformative Schrödinger-Virasoro algebras mainly using the techniques introduced recently by Liu, Pei and Zhu, which indicate that all cases considered in this paper except one behave different from their centerless ones.
In this paper, we study weight representations over the Schr{ö}dinger Lie algebra $\mathfrak{s}_n$ for any positive integer $n$. It turns out that the algebra $\mathfrak{s}_n$ can be realized by polynomial differential operators. Using this realization, we give a complete classification of irreducible weight $\mathfrak{s}_n$-modules with finite dimensional weight spaces for any $n$. All such modules can be clearly characterized by the tensor product of $\mathfrak{so}_n$-modules, $\mathfrak{sl}_2$-modules and modules over the Weyl algebra.
In this paper, we study the derivations, the central extensions and the automorphism group of the extended Schrodinger-Virasoro Lie algebra, introduced by J. Unterberger in the context of two-dimensional conformal field theory and statistical physics. Moreover, we show that the extended Schrodinger-Virasoro Lie algebra is an infinite-dimensional complete Lie algebra and the universal central extension of the extended Schrodinger-Virasoro Lie algebra in the category of Leibniz algebras is the same as that in the category of Lie algebras.
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