Comparaison des homologies du groupe linéaire et de son algèbre de Lie. (Comparison of homologies of a linear group and its Lie algebra)
type: Item
instance of: scholarly article
title: Comparaison des homologies du groupe linéaire et de son algèbre de Lie. (Comparison of homologies of a linear group and its Lie algebra)
zbMATH Open document ID: 0619.20025
author: J.-L. Loday
publication date: 1987-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/74773
review text: The homology of the discrete group \(GL_ n(R)\) for a local ring R behaves like the homology of the Lie algebra \(gl_ n(A)\) for A an associative algebra over a characteristic zero field. The aim of this article is to survey the known results (without giving any proof) about these homology groups and to connect them with algebraic K-theory, cyclic homology and motivic cohomology. Some questions are raised and a definition for an ''additive motivic cohomology theory'' is suggested.
Mathematics Subject Classification ID: 20G10
Mathematics Subject Classification ID: 17B45
Mathematics Subject Classification ID: 17B56
Mathematics Subject Classification ID: 18F25
Mathematics Subject Classification ID: 20G35
zbMATH DE Number: 4004467
zbMATH Keywords: homology groups
zbMATH Keywords: K-theory
zbMATH Keywords: cyclic homology
zbMATH Keywords: motivic cohomology
zbMATH Keywords: homology of general linear groups
MaRDI profile type: Publication
OpenAlex ID: W2083309839
cites work: Q3762432
cites work: Notes on motivic cohomology
cites work: Q3922789
cites work: Algebraic cycles and higher K-theory
cites work: Scissors congruences. II
cites work: Q3667036
cites work: Crossed Simplicial Groups and their Associated Homology
cites work: On the general linear group and Hochschild homology
cites work: Relative algebraic K-theory and cyclic homology
cites work: Q3749217
cites work: Q3749216
cites work: Q3910672
cites work: Q3336376
cites work: Homology stability for linear groups
cites work: A presentation for some 𝐾₂(𝑛,𝑅)
cites work: Central extensions of Lie algebras
cites work: Q5612511
cites work: \(K_ 2\) of non-commutative local rings
cites work: Values of zeta-functions at non-negative integers
cites work: The construction of weight-two arithmetic cohomology
cites work: $K$-théorie algébrique et représentations de groupes
cites work: Q3955554
cites work: Q3919862
cites work: Q5751054
cites work: Cyclic homology and the Lie algebra homology of matrices
cites work: Q5597389
cites work: Values of Zeta Functions of Varieties Over Finite Fields
cites work: Introduction to Algebraic K-Theory. (AM-72)
cites work: Q3696154
cites work: Q5631287
cites work: Zentrale Erweiterungen der speziellen linearen Gruppe eines Schiefkörpers.
cites work: A reciprocity law for \(K_2\)-traces
cites work: Homology of classical Lie groups made discrete. I: Stability theorems and Schur multipliers
cites work: Q3963203
cites work: Q3310033
DOI: 10.5802/AIF.1116
published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 4004467