We construct a non-associative algebra A over a field of characteristic zero with the following properties: if V is the variety generated by A, then V has exponential growth but any proper subvariety of V is nilpotent. Moreover, by studying the asymptotics of the sequence of codimensions of A we deduce that exp(V) = 2.
Mishchenko, S., Valenti, A. (2014). An almost nilpotent variety of exponent 2. ISRAEL JOURNAL OF MATHEMATICS, 199(199), 241-257 [10.1007/s11856-013-0029-4].
An almost nilpotent variety of exponent 2
VALENTI, Angela
2014-01-01
Abstract
We construct a non-associative algebra A over a field of characteristic zero with the following properties: if V is the variety generated by A, then V has exponential growth but any proper subvariety of V is nilpotent. Moreover, by studying the asymptotics of the sequence of codimensions of A we deduce that exp(V) = 2.
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