Discriminant of Symplectic Involutions

Garibaldi, Skip;Parimala, Raman;Tignol, Jean-Pierre
(2009) Pure and Applied Mathematics Quarterly — Vol. 5, n° 1, p. 349-374 (2009)

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Authors
  • Garibaldi, SkipEmory University
    Author
  • Parimala, RamanEmory University
    Author
  • Tignol, Jean-Pierreorcid-logoUCLouvain
    Author
Abstract
We define an invariant of torsors under adjoint linear algebraic groups of type C_n-equivalently, central simple algebras of degree 2n with symplectic involution-for n divisible by 4 that takes values in H^3(F, mu_2). The invariant is distinct from the few known examples of cohomological invariants of torsors under adjoint groups. We also prove that the invariant detects whether a central simple algebra of degree 8 with symplectic involution can be decomposed as a tensor product of quaternion algebras with involution.
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Garibaldi, S., Parimala, R., & Tignol, J.-P. (2009). Discriminant of Symplectic Involutions. Pure and Applied Mathematics Quarterly, 5(1), 349-374. https://doi.org/10.4310/PAMQ.2009.v5.n1.a11 (Original work published 2009)