Verma Modules Over Generalized Block Algebras B(b⁽¹⁾, b⁽²⁾)

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.

Key Words:

• Generalized Block algebra
• Verma module

2000 Mathematics Subject Classification:

• 17B10
• 17B65
• 17B68

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.