Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userWhittaker modules for the Schrodinger-Virasoro algebra
300
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
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 $psi$.
rate research
Read More
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.
In this paper, we define the induced modules of Lie algebra ad$(B)$ associated with a 3-Lie algebra $B$-module, and study the relation between 3-Lie algebra $A_{omega}^{delta}$-modules and induced modules of inner derivation algebra ad$(A_{omega}^{delta})$. We construct two infinite dimensional intermediate series modules of 3-Lie algebra $A_{omega}^{delta}$, and two infinite dimensional modules $(V, psi_{lambdamu})$ and $(V, phi_{mu})$ of the Lie algebra ad$(A_{omega}^{delta})$, and prove that only $(V, psi_{lambda0})$ and $(V, psi_{lambda1})$ are induced modules.
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.
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 nonzero level, our arguments use the Casimir element of semisimple Lie algebra $sl_2$ and the description of simple modules over conformal Galilei algebras by R. L{u}, V. Mazorchuk and K. Zhao.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
