Adjamagbo Determinant and Serre conjecture for linear groups over Weyl algebras

Details Adjamagbo Determinant and Serre conjecture for linear groups over Weyl algebras Adjamagbo Determinant and Serre conjecture for linear groups over Weyl algebras

2008-01-08

arxiv.org/abs/0801.1207v1

Mathematics

K-Theory and Homology

Scientific paper

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 $K_1$-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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