Complete Classifications of Generalized Kac–Moody Algebras Possessing Special Imaginary Roots and Strictly Imaginary Property

Abstract

In this article, we consider all generalized Kac–Moody algebras (GKM algebras) for the purpose of finding out special imaginary roots and strictly imaginary roots. We give a complete classification of GKM algebras possessing special imaginary roots and also give a complete classification of GKM algebras possessing strictly imaginary property (GKM algebras whose imaginary roots are strictly imaginary). We also conclude that the Monster Lie algebra has no special imaginary root and does not satisfy strictly imaginary property.

Key Words:

• Generalized Kac–Moody algebras
• Special imaginary roots
• Strictly imaginary roots

AMS Mathematics Subject Classification (2000):

• 17B67

ACKNOWLEDGMENT

The second author is grateful to the Ramanujan Institute for Advanced Study in Mathematics, University of Madras for having given her a short-term Visiting Fellowship during March 2005 under the Special Assistance Programme of the University Grants Commission (UGC-SAP) of the Government of India. The authors are thankful to the referee whose comments were very useful in writing the final form of the article.

Notes

Communicated by K. C. Misra.