On homotopy invariance for homology of rank two groups.

DOI10.1016/j.jpaa.2012.03.004zbMath1267.20062OpenAlexW2061350790MaRDI QIDQ1934983

Matthias Wendt

Publication date: 30 January 2013

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jpaa.2012.03.004

zbMATH Keywords

elementary subgroupspolynomial ringsChevalley groupsbuildingshomotopy invarianceSteinberg groupshomology of linear groups

Mathematics Subject Classification ID

(K)-theory and homology; cyclic homology and cohomology (19D55) Cohomology theory for linear algebraic groups (20G10) Other homology theories in algebraic topology (55N35) Central extensions and Schur multipliers (19C09) Linear algebraic groups over adèles and other rings and schemes (20G35)

Related Items (6)

The commutators of classical groups ⋮ Multiple commutators of elementary subgroups: end of the line ⋮ On centrality of \(\operatorname{K}_2\) for Chevalley groups of type \(\mathsf{E}_\ell\) ⋮ On centrality of even orthogonal \(\mathrm{K}_2\) ⋮ ${\mathrm A}_3$-proof of structure theorems for Chevalley groups of types ${\mathrm E}_6$ and ${\mathrm E}_7$ II. Main lemma ⋮ Another presentation for symplectic Steinberg groups

Cites Work

• Finiteness properties of arithmetic groups over function fields.
• Homology of linear groups
• An algorithmic proof of Suslin's stability theorem for polynomial rings
• On symplectic groups over polynomial rings
• Solution of the congruence subgroup problem for \(\text{SL}_ n\) \((n\geq 3)\) and \(\text{Sp}_{2n}\) \((n\geq 2)\)
• Reductive groups over a local field
• Buildings
• Whitehead groups of chevalley groups over polynomial rings
• Free quotients of 𝑆𝐿₂(𝑅[𝑥)]
• Generators, Relations and Coverings of Chevalley Groups Over Commutative Rings
• Groups of cohomological dimension one
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