K1 of Chevalley groups are nilpotent

By Roozbeh Hazrat, Nikolai Vavilov. 2003

113 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/705dfa10266c8b8cf3f08672c9c6a3c44cb49a5e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Alexei Stepanov
2. Nikolai Vavilov
3. V. Petrov
4. A. Bak
5. A. Stavrova
6. Benson Farb
7. Roozbeh Hazrat
8. Sergey I. Nikolenko

In Discrete Mathematics and Combinatorics

1. Roozbeh Hazrat
2. Alexei Stepanov
3. V. Petrov
4. Nikolai Vavilov
5. A. Bak
6. A. Stavrova
7. Benson Farb
8. Sergey I. Nikolenko

In Geometry and Topology

1. Roozbeh Hazrat
2. V. Petrov
3. Nikolai Vavilov
4. Alexei Stepanov
5. A. Bak
6. A. Stavrova
7. Benson Farb
8. Sergey I. Nikolenko

Citations in the corpus

• Homotopy invariance of non-stable K_1-functors (2011, background): “ a straightforward extension to isotropic reductive groups of [W, Lemma 2.4] proved for any Chevalley group G. Note that even for Chevalley groups, the groups KG 1 (A) are in general non-abelian (cf. [HV]). Lemma 2.2. Let G be an isotropic reductive group over a commutative ring A (with 1) satisfyin”
• Group actions and Helly's theorem (2008, background): “e G which are k-split . After proving Theorem 1.3, we wondered if G(Φ,R)/E(Φ,R) is always solvable when rank(Φ) ≥ 2, and asked R. Hazrat and N. Vavilov, who then answered this question affirmatively in [HV], as long as R has finite Bass-Serre dimension. Together with Theorem 1.3, this immediately gives”
• Localization–completion strikes again: Relative K1 is nilpotent by abelian (2009, methodology): “In [19], [20] one can find a slightly less technical description of localisation-completion and its detailed comparison with other localisation methods.”
• Structure of Chevalley groups over rings via universal localization (2013, methodology): “) ≤ d, then S (d) δ G(R,a,b) = EE(R,a,b). Thus, the first formula implies the second one. The following straightforward corollary generalizes results of A.Bak, R.Hazrat, and N.Vavilov obtained in [5], [16] and [7]. 20 ALEXEISTEPANOV Corollary 12.8. Let a1,...,ad be ideals of a Noetherian ring R, wher”
• Odd Unitary Groups (2005, background): “In forthcoming papers, the author intends to carry over to the case of odd unitary groups structure theorems and results of elementary K-theory such as the injective stability of K1, the behavior of the group at a stable level (see [7, 8, 19]), the nilpotency of K1 (see [6, 11, 12 ]), and the centr”
• Structure of Chevalley groups: The proof from the book (2007, background): “In [66], [32–34], [57, 45 ], one can find a detailed survey and various new proofs.”