Let B be the universal central extension of a graded Lie algebra of Block type. In this paper, it is proved that any quasifinite irreducible B-module is either highest weight, lowest weight or uniformly bounded. Furthermore, the quasifinite irreducible highest weight B-modules are classified, and the intermediate series B-modules are classified and constructed.
In this paper, Whittaker modules for the Schrödinger-Witt algebra sv are defined. The Whittaker vectors and the irreducibility of the Whittaker modules are studied. sv has a triangular decomposition according to its Cartan subalgebra h: sv = sv − h sv + . For any Lie algebra homomorphism : sv + → C, we can define Whittaker modules of type . When is nonsingular, the Whittaker vectors, the irreducibility, and the classification of Whittaker modules are completely determined. When 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 .
Let Der(C q ) be the derivation Lie algebra of the quantum torus C q . We construct a functor from gl d -modules to Der(C q )-modules, which generalizes the constructions obtained by Shen [Scientia Sinica A 29 (1986) 570], Larsson [Internat. J. Modern Phys. A 7 (1992) 6493], and Rao [J. Algebra 182 (1996) 401]. We also give a complete description of the structure of the Der(C q )-modules when all the entries of the quantum torus matrix q = (q ij ) d×d are roots of unity. 2004 Elsevier Inc. All rights reserved.
In the present paper, we study the nonzero level Harish-Chandra modules for the Virasoro-like algebra. We prove that a nonzero level Harish-Chandra module of the Virasoro-like algebra is a generalized highest weight (GHW for short) module. Then we prove that a GHW module of the Virasoro-like algebra is induced from an irreducible module of a Heisenberg subalgebra.
We develop a theory of toroidal vertex algebras and their modules, and we give a conceptual construction of toroidal vertex algebras and their modules. As an application, we associate toroidal vertex algebras and their modules to toroidal Lie algebras.
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