Classifying \(G\)-graded algebras of exponent two
Let \(G\) be a finite abelian group, and let \(A\) be a \(G\)-graded algebra over an algebraically closed field of characteristic zero. Let \(\mathcal{V}\) be the \(G\)-variety generated by \(A\). The author proves that \(\mathcal{V}\) has \(G\)-exponent greater than 2 if and only if it contains one of the graded algebras given in an explicit list, and that \(\mathcal{V}\) has \(G\)-exponent 2 if and only if it does not contain any of the graded algebras in the previous list and it contains at least one graded algebra in a second explicit list.
scientific article; zbMATH DE number 7015407
scientific article