  We study the dynamical analogue of the matrix algebra M(n), constructed from
a dynamical R-matrix given by Etingof and Varchenko. A left and a right
corepresentation of this algebra, which can be seen as analogues of the
exterior algebra representation, are defined and this defines dynamical quantum
minor determinants as the matrix elements of these corepresentations. These
elements are studied in more detail, especially the action of the
comultiplication and Laplace expansions. Using the Laplace expansions we can
prove that the dynamical quantum determinant is almost central, and adjoining
an inverse the antipode can be defined. This results in the dynamical GL(n)
quantum group associated to the dynamical R-matrix. We study a *-structure
leading to the dynamical U(n) quantum group, and we obtain results for the
canonical pairing arising from the R-matrix.
