Representations of the Quantized Weyl Algebra Associated to the Quantum Plane

Shang-yuan, Lin; Wu, Yuezhu

doi:10.1142/s1005386705000684

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Cited by 7 publications

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“…Since a class of infinite dimensional simple Lie algebras was introduced by Block [B], generalizations of Block algebras have been studied by some authors, partially because they are closely related to the Virasoro algebra or algebras associated quantum plane (e.g., [DZ,LW,OZ,SZ,X1,X2,ZM]).…”

Section: §1 Introductionmentioning

confidence: 99%

Verma Modules over a Block Lie Algebra

Jiang

2008

Algebra Colloq.

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Abstract. Let B be the Lie algebra with basisIt is proved that an irreducible highest weight B-module is quasifinite if and only if it is a proper quotient of a Verma module. For an additive subgroup Γ of F, there corresponds to a Lie algebra B(Γ) of Block type. Given a total order ≻ on Γ and a weight Λ, a Verma B(Γ)-module M (Λ, ≻) is defined. The irreducibility of M (Λ, ≻) is completely determined.

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