Norms and gauges on Clifford Algebra

From a normed quadratic space (V,q), we construct a norm on the Clifford algebra C(V,q). We describe the associated graded form of this norm and give a condition for this norm to be a gauge. Then, we apply our results to prove that for a complete discrete valued field, an anisotropic quadratic form q with dim q = 0 mod 8 and nonsplit Clifford algebra cannot be at the same time a transfer of a K-hermitian form with K/F an inertial quadratic field extension and a transfer of a T-hermitian form with T/F a ramified quadratic field extension.