Identities of bilinear mappings and graded polynomial identities of matrices (Q1399922)

The paper deals with polynomial identities for the bilinear mappings \(V\otimes W\to K\) and \(V_r\otimes V^*_r\to M_r(K)\), where \(V,W,V_r\) are finite dimensional linear spaces over a field \(K\) of characteristic 0, \(\dim V_r =r\), \(V^*\) is the dual of \(V\) and \(M_r(K)\) is the \(r\times r\) matrix algebra. The results are applied to the \(G\)-graded polynomial identities of \(M_r(K)\), where \(G\) is a group. The elementary \(G\)-grading is assocated with the \(r\)-tuple \((g,\dots,g,h)\), where \(g,h\in G\) and \((g^{-1}h)^2\) is not the identity in \(G\).