  An important step in the determination of the automorphism group of the
quantum torus of rank $n$ (or twisted group algebra of $\mathbb Z^n$) is the
determination of its so-called non-scalar automorphisms. We present a new
algorithimic approach towards this problem based on the bivector representation
$\wedge^2 : \mathrm{GL}(n, \mathbb Z) \rightarrow \mathrm{GL}(\binom{n}{2},
\mathbb Z)$ of $\mathrm{GL}(n, \mathbb Z)$ and thus compute the non-scalar
automorphism group $\mathrm{Aut}(\mathbb Z^n, \lambda)$ in several new cases.
As an application of our ideas we show that the quantum polynomial algebra
(multiparameter quantum affine space of rank $n$) has only scalar (or toric)
automorphisms provided that the torsion-free rank of the subgroup generated by
the defining multiparameters is no less than $\binom{n - 1}{2} + 1$ thus
improving an earlier result. We also investigate the question: when is a
multiparameter quantum affine space free of so-called linear automorphisms
other than those arising from the action of the $n$-torus ${(\mathbb
F^\ast)}^n$.
