Past works

• On weight systems derived from Heisenberg Lie algebras
published. ( Journal of Knot Theory and Its Ramifications 12(2003), 589--604)
• On invariant symmetric 2-tensors of nilpotent Lie algebras of maximal rank
It is an experiment to construct a weight system from nilpotent Lie algebras. The properties of symmetric ad-invariant 2-tensors of nilpotent Lie algebras of maximal rank are discussed from the viewpoint of root systems. 2-tensors are calculated explicitly in the cases that the algebras come from the generalized Cartan matrices of finite type.

• The loop-degrees of Jacobi diagrams and Lie algebras [1.5MB, 2/28]
It is a generalization of the papers above. Nilpotent Lie algebras induce weight systems which vanish all Jacobi diagrams except for trees. Certain extensions of nilpotent ones do weight systems which vanish except for trees and wheels. For weight systems derived from algebras of the other types, there exist Jacobi diagrams having sufficiently many loops and not being vanished by the weight systems.

• An invariant of 3-manifolds with value in F₅
(For the proceeding of the workshop "Art of Low Dimensional Topology IV") A modification of the algebra of web diagrams, the coefficients of which are in a field of characteresitic 5, and whose defining relations are IHX, STU, AS, L₁ and P₂, is isomorphic to F₅[[x]], the algebra of formal power series.  There is a projection of the Kontsevich invariant of links to the algebra, and it gives a 3-manifold invariant.