Quadratic forms of dimension 8 with trivial discrimiand and Clifford algebra of index 4

2009/02/06 by Alexandre Masquelein, Anne Quéguiner-Mathieu, Masquelein, Alexandre +3
Mathematics · #11E04 #16K20 #16W10 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Rings and Algebras (math.RA) #math.RA #msc:11E04 #msc:16K20 #msc:16W10

paper · pdf · doi:10.48550/arxiv.0902.1031

arxiv created 2009/02/06 · openalex publication_date 2009/02/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Izhboldin and Karpenko proved in 2000 that any quadratic form of dimension 8 with trivial discriminant and Clifford algebra of index 4 is isometric to the transfer, with respect to some quadratic étale extension, of a quadratic form similar to a 2-fold Pfister form. We give a new proof of this result, based on a theorem of decomposability for degree 8 and index 4 algebras with orthogonal involution.

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