New polynomial identities for 2 × 2 generic matrices in characteristic 2 Original Research Article

Let Rm(K) be the K-algebra generated by the generic 2 × 2 matrices y1,…,ym over a unitary commutative associative ring K. Our main result is that there exists a multilinear element f(y1,…,y5) of degree 5 in Rm(Z) which is in the kernel of the canonical homomorphism image and does not belong to image. This means that there exists a multilinear polynomial identity of degree 5 for the matrix algebra image which does not follow from the polynomial identities of image. Before such a (non-multilinear) identity of degree 6 was found by Schelter.