Serdica Mathematical Journal, Vol. 26, No 3, (2000), 245p-252p
It was recently proved that any variety of associative algebras
over a field of characteristic zero has an integral exponential growth. It is
known that a variety V has polynomial growth if and only if V does not
contain the Grassmann algebra and the algebra of 2 × 2 upper triangular
matrices. It follows that any variety with overpolynomial growth has exponent
at least 2. In this note we characterize varieties of exponent 2 by
exhibiting a finite list of algebras playing a role similar to the one played by
the two algebras above.
∗The first author was partially supported by MURST of Italy; the second author was par-
tially supported by RFFI grant 99-01-00233.