The discriminant of a symplectic involution

Berhuy, Grégory;Monsurrò, Marina;Tignol, Jean-Pierre
(2003) Pacific Journal of Mathematics — Vol. 209, n° 2, p. 201-218 (2003)

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  • Berhuy, GrégoryEcole Polytechnique Fédérale de Lausanne
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  • Monsurrò, MarinaEcole Polytechnique Fédérale de Lausanne
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  • Tignol, Jean-Pierreorcid-logoUCLouvain
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Abstract
An invariant for symplectic involutions on central simple algebras of degree divisible by 4 over fields of characteristic different from 2 is defined on the basis of Rost's cohomological invariant of degree 3 for torsors under symplectic groups. We relate this invariant to trace forms and show how its triviality yields a decomposability criterion for algebras of degree 8 with symplectic involution.
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Berhuy, G., Monsurrò, M., & Tignol, J.-P. (2003). The discriminant of a symplectic involution. Pacific Journal of Mathematics, 209(2), 201-218. https://doi.org/10.2140/pjm.2003.209.201 (Original work published 2003)