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Verma modules over Virasoro-like algebras

Published online by Cambridge University Press:  09 April 2009

Xian-Dong Wang
Affiliation:
Department of Mathematics, Qingdao University, Qingdao 266071, P. R., China, e-mail: wanxd@public.qd.sd.cn
Kaiming Zhao
Affiliation:
Department of Mathematics, Wilfrid Laurier University, WaterlooOntario N2L 3C5, Canada, and Institute of Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, P. R., China, e-mail: kzhao@wlu.ca
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Abstract

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Let K be a field of characteristic 0, G the direct sum of two copies of the additive group of integers. For a total order ≺ on G, which is compatible with the addition, and for any ċ1, ċ2K, we define G-graded highest weight modules M1, ċ2, ≺) over the Virasoro-like algebra , indexed by G. It is natural to call them Verma modules. In the present paper, the irreducibility of M1, ċ2, ≺) is completely determined and the structure of reducible module M1, ċ2, ≺)is also described.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2006

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