Uncolouring of Lie colour algebras

Abstract

The link between a Lie colour algebra and a corresponding Lie superalgebra is clarified in the case of the general linear algebras. The Lie superalgebra inherits from the colour cocommutative coproduct of the corresponding Lie colour algebra, a super coproduct which differs from the usual one, and is not supercocommutative. It is associated with a new R-matrix satisfying the super Yang-Baxter equation.