Determinant-like functions for matrices over finite-dimensional division algebras (Q2708732)

Let \(D\) be a division algebra over its centre \(F\), \((D:F)=n\), and \(A=M_n(D)\), then \(A^*=\text{GL}_n(D)\) is equipped with a multiplicative function, namely, the reduced norm of \(A\) to \(F\). It is known that the difference between the reduced norm and the Dieudonné determinant is measured to a large extend by the reduced Whitehead group \(SK_1(D)\) and the cokernel of the reduced norm. The aim of this paper is to introduce certain multiplicative maps on \(A^*\) and to investigate their properties with respect to the above mentioned functions via reduced \(K\)-theory.NEWLINENEWLINEFor the entire collection see [Zbl 0949.00018].