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 \(\exp(\mathcal V)=2\).


17A30 Nonassociative algebras satisfying other identities
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