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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 intermediate series over the twisted Heisenberg-Virasoro algebra is of the form $mathcal{A}_{a,b,c}$ for $ain mathbb{R}, bin 1/2+sqrt{-1}mathbb{R}, cin mathbb{C}.$
2-local derivation is a generalized derivation for a Lie algebra, which plays an important role to the study of local properties of the structure of the Lie algebra. In this paper, we prove that every 2-local derivation on the twisted Heisenberg-Virasoro algebra is a derivation.
In this paper, we classify all indecomposable Harish-Chandra modules of the intermediate series over the twisted Heisenberg-Virasoro algebra. Meanwhile, some bosonic modules are also studied.
In this paper, Whittaker modules for the Schrodinger-Virasoro algebra $mathfrak{sv}$ are defined. The Whittaker vectors and the irreducibility of the Whittaker modules are studied. $mathfrak{sv}$ has a triangular decomposition according to the Cartan
We first determine the automorphism group of the twisted Heisenberg-Virasoro vertex operator algebra $V_{mathcal{L}}(ell_{123},0)$.Then, for any integer $t>1$, we introduce a new Lie algebra $mathcal{L}_{t}$, and show that $sigma_{t}$-twisted $V_{mat
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 al