Polynomial identities for \(2\times 2\) matrices with finite group actions. (Q1429902)

Let \(G\) be a finite group acting faithfully on \(M_2\), the algebra of \(2\times 2\) matrices over the complex field. Then \(G\) is a subgroup of \(\text{PGL}_2\) and according to the description of the finite subgroups of \(\text{PGL}_2\) it follows that \(G\) is either cyclic, or dihedral, or \(A_4\), \(A_5\), \(S_4\). The paper deals with the \(G\)-identities of \(M_2\). In each of the cases for \(G\), a finite basis of the \(G\)-identities is constructed.