Comparaison des homologies du groupe linéaire et de son algèbre de Lie
Annales de l'Institut Fourier, Volume 37 (1987) no. 4, p. 167-190

The homology of the discrete groupe 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 “addivitive motivic cohomology theory” is suggested.

Pour un anneau local R l’homologie du groupe discret GL n (R) a un comportement tout à fait analogue à l’homologie de l’algèbre de Lie gl n (A) lorsque A est une algèbre associative sur un corps de caractéristique zéro. L’objet de cet article est de faire une synthèse (sans démonstration) des résultats connus sur ces groupes d’homologie en exhibant leurs liens avec la K-théorie algébrique, l’homologie cyclique et la cohomologie motivique. On y pose un certain nombre de questions et on propose une définition pour l’analogue additif de la cohomologie motivique.

@article{AIF_1987__37_4_167_0,
     author = {Loday, Jean-Louis},
     title = {Comparaison des homologies du groupe lin\'eaire et de son alg\`ebre de Lie},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Durand},
     address = {28 - Luisant},
     volume = {37},
     number = {4},
     year = {1987},
     pages = {167-190},
     doi = {10.5802/aif.1116},
     zbl = {0619.20025},
     mrnumber = {89i:17011},
     language = {fr},
     url = {http://www.numdam.org/item/AIF_1987__37_4_167_0}
}
Loday, Jean-Louis. Comparaison des homologies du groupe linéaire et de son algèbre de Lie. Annales de l'Institut Fourier, Volume 37 (1987) no. 4, pp. 167-190. doi : 10.5802/aif.1116. http://www.numdam.org/item/AIF_1987__37_4_167_0/

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