Decomposability of orthogonal involutions in degree 12
(2020) Pacific Journal of Mathematics — Vol. 304, n° 1, p. 169-180 (2020)
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- Authors
Tignol, Jean-Pierre 
- Abstract
- A theorem of Pfister asserts that every 12-dimensional quadratic form with trivial discriminant and trivial Clifford invariant over a field of characteristic different from 2 decomposes as a tensor product of a binary quadratic form and a 6-dimensional quadratic form with trivial discriminant. Our main result extends Pfister’s result to orthogonal involutions: every central simple algebra of degree 12 with orthogonal involution of trivial discriminant and trivial Clifford invariant decomposes into a tensor product of a quaternion algebra and a central simple algebra of degree 6 with orthogonal involutions. This decomposition is used to establish a criterion for the existence of orthogonal involutions with trivial invariants on algebras of degree 12, and to calculate the f3-invariant of the involution if the algebra has index 2.
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Citations
Quéguiner-Mathieu, A., & Tignol, J.-P. (2020). Decomposability of orthogonal involutions in degree 12. Pacific Journal of Mathematics, 304(1), 169-180. https://doi.org/10.2140/pjm.2020.304.169 (Original work published 2020)