SIMPLE, PRIMITIVE, AND STRONGLY PRIME JORDAN 3-GRADED LIE ALGEBRAS

Abstract

In this paper we give full descriptions of Jordan 3-graded Lie algebras under conditions of simplicity, primitivity and strong primeness. For nondegenerate Jordan 3-graded Lie algebras, we also prove that their heart is either zero or simple.

Key Words:

• 3-graded Lie algebras
• Heart
• Structure theory

Mathematics Subject Classification:

• 17B60
• 17B05
• 17C10

ACKNOWLEDGMENTS

The author would like to thank Prof. J. A. Anquela and Prof. T. Cortés for their careful reading of this manuscript and their valuable suggestions and comments. She is also greatly indebted to Prof. E. Zelmanov for his interesting remarks and suggestions.

The author is partially supported by the DGES and Fondos FEDER, PB97-1069-C02-02, the MCYT and Fondos FEDER, BFM2001-1938-C02-02, and an F.P.I. Grant (MCYT).

Notes

^#Communicated by E. Zelmamov.

^‡Part of the author's doctoral thesis supervised by Prof. J. A. Anquela and Prof. T. Cortés.