2 thoughts on “Trivial anti-associativity”

  1. alejosalvatore says:

    I wonder why no one ever answered this. Just go round the diagram from the pentagon axiom once. For instance,
    ((ab)c)d=-(a(bc))d=a((bc)d)=-a(b(cd))=(ab)(cd)=-((ab)c)d.
    Since the characteristic is different from two, this implies that ((ab)c)d=0.

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  2. Echoing the other comment, the secret is to use Buchberger’s algorithm on the overlap given by the left comb. Then, rewriting using the anti-associative rule, one obtains that twice the fourfold product is zero, which adds a relation, as expected.

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