On almost polynomial growth of proper central polynomials (Q6621273)

Based on authors' abstract: To any associative algebra \(A\) is associated a numerical sequence \(c_n(A)\), \(n\ge 1\), called \textit{the sequence of proper central codimensions of \(A\)}. It gives information on the growth of the proper central polynomials of the algebra. If \(A\) is a PI-algebra over a field of characteristic zero it has been recently shown that such a sequence either grows exponentially or is polynomially bounded. The authors classify, up to PI-equivalence, the algebras \(A\) for which the sequence \(c_n(A)\), \(n\ge 1\), has almost polynomial growth. Then they face a similar problem in the setting of group-graded algebras and they obtain a classification also in this case when the corresponding sequence of proper central codimensions has almost polynomial growth.\N\NHow is the classification done? As usual in this type of problems, via some minimal algebras\N\NTheorem 2.3. Let \(A\) be a PI-algebra such that \(\exp\delta(A)\ge 2\). Then \(Id(A)\subseteq Id(D)\) or \(Id(A) \subseteq Id(D_0)\) or \(Id(A)\subseteq Id(E)\).\N\N(See definitions of algebras \(D\), \(D_0\), \(E\) on the pages 4571, 4572, 4573.)