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Subsections

## 3.3 Constancy conditions or

### 3.3.1 Statement of the result

Definition 3.4   Let be the unital commutative algebra over generated by symbols Yijk for distinct indices , modulo the anti-cyclicity relations Yijk=Y-1jik=Yjki.

Warning 3.5   Below we will mostly regard as an -module, and not as an algebra. Thus we will only use the product of as a convenient way of writing certain elements and linear combinations of elements. The subspaces of that we will consider will be subspaces in the linear sense, but not ideals or subalgebras, and similarly for quotients and maps from or to .

It is easy to define a map . For an n-link L set

It follows from Section 3.2.3 that this definition descends to the quotient of by the co-derivatives of (n+1)-links.

Theorem 4   The thus defined map is an isomorphism.

### 3.3.5 Reducing third commutators

TBW.

Next: 3.4 Integrability conditions or Up: 3. The case of Previous: 3.2 Preliminaries
Dror Bar-Natan
2000-03-19