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Verma modules over Virasoro-like algebras
- Part of
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- Journal:
- Journal of the Australian Mathematical Society / Volume 80 / Issue 2 / April 2006
- Published online by Cambridge University Press:
- 09 April 2009, pp. 179-191
- Print publication:
- April 2006
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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, ċ2 ∈ K, we define G-graded highest weight modules M(ċ1, ċ2, ≺) over the Virasoro-like algebra
, indexed by G. It is natural to call them Verma modules. In the present paper, the irreducibility of M (ċ1, ċ2, ≺) is completely determined and the structure of reducible module M (ċ1, ċ2, ≺)is also described.
, indexed by 