Quasifinite representations of a class of Block type Lie algebras $\BB$

Details Quasifinite representations of a class of Block type Lie algebras $\BB$ Quasifinite representations of a class of Block type Lie algebras $\BB$

2011-02-25

arxiv.org/abs/1102.5187v1

Mathematics

Representation Theory

LaTeX, 22 pages

Scientific paper

Intrigued by a well-known theorem of Mathieu's on Harish-Chandra modules over the Virasoro algebra, we give an analogous result for a class of Block type Lie algebras $\BB$, where the parameter $q$ is a nonzero complex number. We also classify quasifinite irreducible highest weight $\BB$-modules and irreducible $\BB$-modules of the intermediate series. In particular, we obtain that an irreducible $\BB$-module of the intermediate series may be a nontrivial extension of a $\Vir$-module of the intermediate series if $q$ is half of a negative integer, where $\Vir$ is a subalgebra of $\BB$ isomorphic to the Virasoro algebra.

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