Structure and Root Multiplicities for Two Classes of Extended Hyperbolic Kac–Moody Algebras and for all Cases

Abstract

In this article, we give a realization, determine the homology modules, the structure of maximal ideals, and also compute the root multiplicities for two classes of extended hyperbolic Kac–Moody algebras and for all cases in general.

Key Words:

• Extended hyperbolic Kac–Moody algebras
• Root multiplicities

2000 Mathematics Subject Classification:

• 17B67

ACKNOWLEDGMENTS

The first author, N. Sthanumoorthy, is grateful to the University Grants Commission (UGC), Apex body of the Government of India, for the financial assistance given under the Major Research Project F. No. 36-272/2008(SR). The second author, A. Uma Maheswari wishes to acknowledge the University Grants Commission, New Delhi, for its financial sanction under the Minor Research Project. The authors are also thankful to the referee whose comments were useful in correcting a few typos found in the initial version of the article.

Notes

Communicated by K. C. Misra.