On Cartan Invariants and Blocks of Zassenhaus Algebras^#

^#Communicated by K. Misra.

In this article, we determine the Cartan invariants for Zassenhaus algebras W(1,n). This is done by reducing representations of generalized restricted Cartan type Lie algebra W(1,n) to representations of restricted Lie algebras W(1,1) and of ± b𝔰 ± b𝔩(2), and then extending Feldvoss-Nakano's argument on W(1,1) to the case W(1,n).

Keywords:

• Generalized restricted Lie algebras
• Zassenhaus algebras (Cartan type Lie algebras)

2000 Mathematics Subject Classification:

• Primary 17B10, 17B50
• Secondary 17B70

ACKNOWLEDGMENTS

A part of this work was done during the “Lie Theory Program” at Chen Xing Mathematics Center in Summer 2001. The authors would like to thank the organizers, Professor Nanhua Xi and Professor Kaiming Zhao, for their invitation. Moreover, they would like to thank Professor Guang-Yu Shen for his helpful conversation. At last, the authors would like to thank the referee for his/her many helpful comments and suggestions for correction. Supported in part by FYTEF (Grant No: 71001), NSF of China (Grant No: 10271047), the Doctoral Program Foundation of EMC and the Shanghai priority academic discipline.

Notes

^#Communicated by K. Misra.