The center of the generic algebra of degree p

2007/04/25 by Esther Beneish, Beneish, Esther
Mathematics · #Advanced Topics in Algebra #Commutative Algebra and Its Applications #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #primary: 13A50 #secondary 20C10

paper · pdf · doi:10.48550/arxiv.0704.3450

openalex publication_date 2007/04/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let F be an algebraically closed field of characteristic zero, and let p be an odd prime. We show that the center of the generic division algebra of degree p is stably rational over F. Equivalently, if we let V=M_p(F) ⊕ M_p(F) and PGL_p act on V by simultaneous conjugation, then we show that the function field of the quotient variety V/PGL_p is stably rational over F.

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