TRACE IDENTITIES AND CENTRAL POLYNOMIALS IN THE MATRIX SUPERALGEBRAS Mn,k

A complete description is given of trace identities for matrix superalgebras where and are square matrices of orders and respectively over the even elements of a Grassmann algebra with countably many generators, while and are and rectangular matrices respectively over the odd elements of . A relation is found between multilinear trace identities of degree in the algebra and irreducible representations of a symmetric group of order . It is proved that over a field of characteristic zero all trace identities of follow from identities of degree that hold in that algebra. For every algebra over a field of arbitrary characteristic a central polynomial is given explicitly.Bibliography: 7 titles.