Universal weight systems from a minimal ℤ22-graded lie algebra

Color Lie algebras, which were introduced by Ree, are a graded extension of Lie (super)algebras by an abelian group. We show that the color Lie algebras can be used to construct universal weight systems for knot invariants of Vassiliev and Kontsevich. As a simple example, we take [Formula: see text] as the grading group and consider the four-dimensional color Lie algebra called [Formula: see text]. The weight system constructed from [Formula: see text] is studied in some detail and some relations between the weights, such as the recurrence relation for chord diagrams, are derived. These relations show that the weight system from [Formula: see text] is a hybrid of those from [Formula: see text] and [Formula: see text].