ABSTRACT
Given a field F with characteristic zero, a free Abelian group G with rank two, and a total order ≺ on G which is compatible with the addition, we define Verma modules M([ddot], ≺) over the generalized Block algebra B(b (1), b (2)) with b (1), b (2) ∈ F. The irreducibility of the module M([ddot], ≺) is completely determined in this article.
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ACKNOWLEDGMENTS
The research was supported by NSF (Grant No. 10171064) of China. This work was carried out during the author's visit to the Institute of Mathematics and System Sciences of the Academy of China. The author would like to thank Prof. Kaiming Zhao and Dr. Rencai Lu for many helpful discussions.
Notes
Communicated by B. Parshall.