  We give simple formulas for the elements $c_k$ appearing in a quantum
Cayley-Hamilton formula for the reflection equation algebra (REA) associated to
the quantum group $U_q(\mathfrak{gl}_N)$, answering a question of Kolb and
Stokman. The $c_k$'s are certain canonical generators of the center of the REA,
and hence of $U_q(\mathfrak{gl}_N)$ itself; they have been described by
Reshetikhin using graphical calculus, by Nazarov-Tarasov using quantum
Yangians, and by Gurevich, Pyatov and Saponov using quantum Schur functions;
however no explicit formulas for these elements were previously known.
  As byproducts, we prove a quantum Girard-Newton identity relating the $c_k$'s
to the so-called quantum power traces, and we give a new presentation for the
quantum group $U_q(\mathfrak{gl}_N)$, as a localization of the REA along
certain principal minors.
