On some minimal supervarieties of exponential growth.
Let \(F\) be a field of characteristic \(0\), a variety of (associative) PI superalgebras over \(F\) is minimal of superexponent \(d\) if its exponent equals \(d\) and each proper subvariety is of superexponent \(<d\). Recall that the exponent is the limit (\(m\to\infty\)) of the \(m\)-th root of the \(m\)-th codimension. The main result of the paper under review states that every minimal variety of superalgebras of finite basic rank is generated by an algebra of a concrete list, called minimal superalgebras. On the other hand it is proved that if \(A\) is a minimal superalgebra whose semisimple part decomposes as a direct sum of graded simple components that are simple, then \(A\) generates a minimal supervariety. The same is shown to be true when the semisimple part of \(A\) consists of exactly two graded simple components.
scientific article; zbMATH DE number 6154885