Existence and uniqueness of \(\sigma\)-forms on finite-dimensional modules (Q2754840)

Let \(K\) be an algebraically closed field and let \(\sigma\) be an involutive automorphism. Let \(A\) be an associative algebra over \(K\) with a \(\sigma\)-linear involution, and let \(M\) be an \(A\)-module. The authors find conditions under which \(M\) admits a non-degenerate binary form, linear with respect to the first variable, and \(\sigma\)-linear with respect to the second one, so that \(M\) becomes unitarizable. The uniqueness of this form is investigated. Several examples and conjectures are given.