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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 algebra $mathfrak{h}:$ $$mathfrak{sv}=mathfrak{sv}^{-}oplusmathfrak{h}oplusmathfrak{sv}^{+}.$$ For any Lie algebra homomorphism $psi:mathfrak{sv}^{+}tomathbb{C}$, we can define Whittaker modules of type $psi.$ When $psi$ is nonsingular, the Whittaker vectors, the irreducibility and the classification of Whittaker modules are completely determined. When $psi$ is singular, by constructing some special Whittaker vectors, we find that the Whittaker modules are all reducible. Moreover, we get some more precise results for special $psi$.
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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 $ain mathbb{R}, bin 1/2+sqrt{-1}mathbb{R}, cin mathbb{C}.$
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.
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A 3-bracket variant of the Virasoro-Witt algebra is constructed through the use of su(1,1) enveloping algebra techniques. The Leibniz rules for 3-brackets acting on other 3-brackets in the algebra are discussed and verified in various situations.
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