Certain invariants of generic matrix algebras

Abstract

Let \(K\) be a field of characteristic zero, \(W\) be the associative unital algebra generated by two generic traceless matrices \(X,\) \(Y.\) We also handle the Lie subalgebra \(L\) of the algebra \(W\) consisting of its Lie elements. Consider the subgroup \(G=\langle e_{21}-e_{12}\rangle\) of the special linear group \(SL_2(K)\) of order 4. In this study, we give free generators of the algebras \(W^G\) and \(L^G\) of invariants of the group \(G\) as a \(C(W)^G\)-module.