Chain equivalences for symplectic bases, quadratic forms and tensor products of quaternion algebras
(2015) Journal of Algebra and its Applications — Vol. 14, n° 3, p. 1-9 (2015)
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- Abstract
- We present a set of generators for the symplectic group which is different from the wellknown set of transvections, from which the chain equivalence for quadratic forms in characteristic 2 is an immediate result. Based on the chain equivalences for quadratic forms, both in characteristic 2 and not 2, we provide chain equivalences for tensor products of quaternion algebras over fields with no nontrivial 3-fold Pfister forms. The chain equivalence for biquaternion algebras in characteristic 2 is also obtained in this process, without any assumption on the base-field.
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Chapman, A. (2015). Chain equivalences for symplectic bases, quadratic forms and tensor products of quaternion algebras. Journal of Algebra and its Applications, 14(3), 1-9. https://doi.org/10.1142/S0219498815500309 (Original work published 2015)