Generic algebras with involution of degree 8m

2001/02/28 by David J. Saltman, Jean-Pierre Tignol, Saltman, David J. +1
Mathematics · #12E15 #14L24 #14L30 #16K20 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.math/0102228

openalex publication_date 2001/02/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The centers of the generic central simple algebras with involution are interesting objects in the theory of central simple algebras. These fields also arise as invariant fields for linear actions of projective orthogonal or symplectic groups. In this paper, we prove that when the characteristic is not 2, these fields are retract rational, in the case the degree is 8m and m is odd. We achieve this by proving the equivalent lifting property for the class of central simple algebras of degree 8m with involution. A companion paper ([S3]) deals with the case of m, 2m and 4m where stronger rationality results are proven.

Citations

• The invariant theory of n × n matrices

Related

• Invariant Fields of Symplectic and Orthogonal Groups
• The center of the generic algebra of degree p
• Characteristic polynomials of central simple algebras
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• Essential Dimension of Central Simple Algebras when the Characteristic is Bad