Norms and gauges on Clifford algebra

Coyette, Cécile
(2018) Communications in Algebra — Vol. 46, n° 10, p. 4355-4376 (2018)

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Authors
  • Coyette, CécileUCLouvain
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Abstract
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.
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Coyette, C. (2018). Norms and gauges on Clifford algebra. Communications in Algebra, 46(10), 4355-4376. https://doi.org/10.1080/00927872.2018.1444166 (Original work published 2018)