Past works
I, NISHIHARA Hideaki, am interested in quantum invariants of tangles,
and weight systems derived from algebras.
- 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
F_{5}
(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, L_{1} and P_{2},
is isomorphic to F_{5}[[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.
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