Totally decomposable symplectic and unitary involutions

2016/03/02 by Andrew E. Dolphin, Andrew Dolphin, Dolphin, Andrew
Mathematics · #11E39 #11E81 #12F05 #16K20 #16W10 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:11E39 #msc:11E81 #msc:12F05 #msc:16K20 #msc:16W10

paper · pdf · doi:10.48550/arxiv.1603.00733

11 pages

arxiv created 2016/03/02 · openalex publication_date 2016/03/02 · arxiv updated 2016/03/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study totally decomposable symplectic and unitary involutions on central simple algebras of index 2 and on split central simple algebras respectively. We show that for every field extension, these involutions are either anisotropic or hyperbolic after extending scalars, and that the converse holds if the algebras are of 2-power degree. These results are new in characteristic 2, otherwise were shown in [3] and [6] respectively.

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