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In this paper, conjugate-linear anti-involutions and unitary Harish-Chandra modules over the Schr{o}dinger-Virasoro algebra are studied. It is proved that there are only two classes conjugate-linear anti-involutions over the Schr{o}dinger-Virasoro algebra. The main result of this paper is that a unitary Harish-Chandra module over the Schr{o}dinger-Virasoro algebra is simply a unitary Harish-Chandra module over the Virasoro algebra.
In this paper, the conjugate-linear anti-involutions and the 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 intermed
In this paper, the property and the classification the simple Whittaker modules for the schr{o}dinger algebra are studied. A quasi-central element plays an important role in the study of Whittaker modules of level zero. For the Whittaker modules of n
Let $mathbb{F}$ be a field of characteristic 0, $G$ an additive subgroup of $mathbb{F}$, $alphain mathbb{F}$ satisfying $alpha otin G, 2alphain G$. We define a class of infinite-dimensional Lie algebras which are called generalized Schr{o}dinger-Vira
In the present paper, using the technique of localization, we determine the center of the quantum Schr{o}dinger algebra $S_q$ and classify simple modules with finite-dimensional weight spaces over $S_q$, when $q$ is not a root of unity. It turns out
In this paper, we study weight representations over the Schr{o}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