Lie pseudoalgebra on graded Hopf algebra

In this paper, we study the structure of Lie pseudoalgebras based on color Lie algebras. We define the [Formula: see text]-graded [Formula: see text]-Lie [Formula: see text]-pseudoalgebra with a grading group [Formula: see text] and its commutation factor [Formula: see text], and with the universal enveloping algebra [Formula: see text] of a color Lie algebra [Formula: see text]. In addition, we define the primitive pseudoalgebras of type W and type S with the color Lie algebra [Formula: see text].