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Timeline for Is there a $3$-commutative algebra?

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Oct 6, 2022 at 6:39 comment added Vladimir Dotsenko @DenisSerre - yes, indeed, I completely agree. Still, it is perhaps useful to have this perspective also, since studying weak identities of various kinds has been at heart of several important breakthroughs in the PI theory in the past. In particular, this observation about $W_1$ came about in a current research project, and I find this instance of 3-commutativity one of the most natural I have seen so far :)
Oct 5, 2022 at 20:05 history edited LSpice CC BY-SA 4.0
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Oct 5, 2022 at 14:50 comment added Denis Serre I agree the calculation, but this subspace $W_1$ is not by itself an algebra (as you noticed, only a Lie algebra). Thus it does not answer my question.
Oct 5, 2022 at 14:40 history answered Vladimir Dotsenko CC BY-SA 4.0