English

Adjamagbo Determinant and Serre conjecture for linear groups over Weyl algebras

K-Theory and Homology 2008-01-09 v1 Rings and Algebras

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 K1K_1-analogue of the well-known Serre Conjecture and asserting that for any integer nn greater than 2, any nn by nn 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

Keywords

Cite

@article{arxiv.0801.1207,
  title  = {Adjamagbo Determinant and Serre conjecture for linear groups over Weyl algebras},
  author = {Kossivi Adjamagbo},
  journal= {arXiv preprint arXiv:0801.1207},
  year   = {2008}
}
R2 v1 2026-06-21T10:00:43.327Z