J. Aust. Math. Soc.  80 (2006), 179-191
Verma modules over Virasoro-like algebras

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


Abstract
Let $\mathbb{K}$ be a field of characteristic 0, G the direct sum of two copies of the additive group of integers. For a total order $\prec$ on G, which is compatible with the addition, and for any $\dot c_1,\dot c_2\in \mathbb{K}$, we define G-graded highest weight modules ${M}(\dot c_1,\dot c_2, \prec)$ over the Virasoro-like algebra $\bar L$, indexed by G. It is natural to call them Verma modules. In the present paper, the irreducibility of ${M}(\dot c_1,\dot c_2, \prec)$ is completely determined and the structure of reducible module ${M}(\dot c_1,\dot c_2, \prec)$ is also described.
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