Adjamagbo Determinant and Serre conjecture for linear groups over Weyl algebras

2008/01/08 by Kossivi Adjamagbo, Adjamagbo, Kossivi
Mathematics · #FOS: Mathematics #K-Theory and Homology (math.KT) #Rings and Algebras (math.RA) #math.KT #math.RA

paper · pdf · doi:10.48550/arxiv.0801.1207

arxiv created 2008/01/08 · arxiv updated 2009/12/01

Abstract

Thanks to the theory of determinants over an Ore domain, also called Adjamagbo determinant by the Russian school of non commutative algebra, we extend to any Weyl algebra over a field of characteristic zero Suslin theorem solving what Suslin himself called the K₁-analogue of the well-known Serre Conjecture and asserting that for any integer n greater than 2, any n by n matrix with coefficients in any algebra of polynomials over a field and with determinant one is the product of elementary matrices with coefficients in this algebra

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