Chain Equivalences for Symplectic Bases, Quadratic Forms and Tensor Products of Quaternion Algebras

2013/12/05 by Adam Chapman, Chapman, Adam
Mathematics · #15A63 #20G35 #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:11E81 #msc:15A63 #msc:16K20 #msc:20G35 #primary 16K20 #secondary 11E81

paper · pdf · doi:10.48550/arxiv.1312.1676

10 pages

arxiv created 2015/01/18 · arxiv updated 2015/01/20

Abstract

We present a set of generators for the symplectic group which is different from the well-known 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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