J. Aust. Math. Soc.
80 (2006), 179191

Verma modules over Virasorolike algebras

XianDong Wang
Department of Mathematics
Qingdao University
Qingdao 266071
P. R. China
wanxd@public.qd.sd.cn



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
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
, we define
Ggraded highest weight modules
over the Virasorolike algebra
, indexed by
G. It is natural to call them Verma modules. In
the present paper, the irreducibility of
is completely determined and the structure of
reducible module
is also described.

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