La forme trace d'une algèbre simple centrale de degré 4
(2006) Comptes rendus - Mathématique — Vol. 342, n° 2, p. 83-87 (2006)
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- Let k be a field of characteristic different from 2 containing a primitive 4-th root of unity. We show that the trace quadratic form of any central simple k-algebra A of degree 4 decomposes in the Witt group of k as the sum of a 2-fold Pfister form q_2 and a 4-fold Pfister form q_4 which are uniquely determined by A. The form q_2 is the norm form of the quaternion algebra Brauer-equivalent to A^2, and q_4 is hyperbolic if and only if A is a symbol algebra.
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Rost, M., Serre, J.-P., & Tignol, J.-P. (2006). La forme trace d’une algèbre simple centrale de degré 4. Comptes rendus - Mathématique, 342(2), 83-87. https://doi.org/10.1016/j.crma.2005.11.002 (Original work published 2006)