Comparaison des homologies du groupe linéaire et de son algèbre de Lie. (Comparison of homologies of a linear group and its Lie algebra)
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.
scientific article; zbMATH DE number 4004467
scientific article