## An almost nilpotent variety of exponent 2.(English)Zbl 1322.17001

Summary: We construct a nonassociative algebra $$A$$ over a field of characteristic zero with the following properties: if $$\mathcal V$$ is the variety generated by $$A$$, then $$\mathcal V$$ has exponential growth but any proper subvariety of $$\mathcal V$$ is nilpotent. Moreover, by studying the asymptotics of the sequence of codimensions of $$A$$ we deduce that $$\exp(\mathcal V)=2$$.

### MSC:

 17A30 Nonassociative algebras satisfying other identities
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### References:

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