Derivation Simple Color Algebras and Semisimple Lie Color Algebras

Abstract

Let K be an algebraically closed field of arbitrary characteristic and Γ an abelian multiplicative group equipped with a bicharacter ε: Γ × Γ → K*. It is proved that, for any finite-dimensional derivation simple color algebra A over K, there exists a simple color algebra S and a color vector space V such that A≅ S⊗ S^ε(V), where S^ε(V) is the ε-symmetric algebra of V. As an application of this result, a necessary and sufficient condition such that a Lie color algebra is semisimple is obtained.

Key Words:

• Derivation simple color algebras
• ε-Symmetric algebras
• Semisimple Lie color algebras

2000 Mathematics Subject Classification:

• 17A36
• 17A60
• 17B05
• 17B75

ACKNOWLEDGMENT

The article was supported by the Education Office of Jiangsu Province (04KJB110001).

Notes

Communicated by K. C. Misra.