Generalized $S-$Type Lie Algebras

The generalized W -type Lie algebra W (e ±x 1 , . . ., e ±x m , m) is introduced in the paper [5] using exponential functions.We define generalized S-type Lie algebras S(e ±x 1 , . . ., e ±x m , m) over F and S p (e ±x 1 , . . ., e ±x m , m) over F p .We show that the Lie algebras S(e ±x 1 , . . ., e ±x m , m) and S p (e ±x 1 , . . ., e ±x m , m) are simple.