Multiparametric quantum deformation of the general linear supergroup (Q1120641)

A matrix with entries in a supercoalgebra is called multiplicative, if the coproduct is modelled by matrix multiplication. The author constructs a superbialgebra \(E_ q\), which is a deformation of a commutative superbialgebra with deformation parameters \(q=\| q_{ij}\|\) making an \(n\times n\)-matrix of prescribed \({\mathbb{Z}}_ 2\)-shape multiplicative. He proves uniqueness of \(E_ q\) and defines a ``universal Hopf extension'' \(H_ q\) of \(E_ q\), the ``general linear quantum group''. The quantum Berezinian is constructed as an element of some factorization of \(H_ q\). There are statements on the structure of \(E_ q\). The reader should be careful for several misprints.