The algebra of Chinese characters in knot theory is the graded algebra 
over the rational numbers spanned by bare Jacobi
diagrams, modulo the antisymmetry and IHX relations. Its multiplication
is disjoint union, its unit
is the empty diagram, and its grading is half the number of vertices
(Bar-Natan 1995, author version, p. 8; Bar-Natan et al. 2000, pp. 219-221).
The antisymmetry relation changes the sign of a diagram when the cyclic order at one trivalent vertex is reversed. To
state IHX without a drawing, fix four external edge
ends 
.
Let 
be the local fragment of two trivalent vertices joined
by an edge 
, with cyclic orders 
and 
. The IHX relation is
 |
with the diagram outside the four external edge ends unchanged. These are relations on bare diagrams without a supporting skeleton.
Let 
be the algebra of chord diagrams with
the four-term relations and without the one-term relation. The symmetrization map
 |
obtained by averaging all orders of attachment of the legs to an oriented supporting circle, is a graded vector
space isomorphism. It does not in general preserve
multiplication. For unframed knots,
compose 
with the quotient map imposing the one-term relation
(Chmutov and Duzhin 2005, pp. 2-3).
