Homology of centralizers

摘要

Given a group Pi, we study the group homology of centralizers Pi(g) g epsilon Pi, and of their central quotients Pi g/(g). This study is motivated by the structure of the Hochschild and the cyclic homology of group algebras, and is based on Quillen's approach to the cyclic homology of algebras via algebra extensions. A method of computing the de Rham complex of a group algebra by means of a Gruenberg resolution is also developed.