Goodwillie, Thomas G. On the general linear group and Hochschild homology. (English) Zbl 0566.20021 Ann. Math. (2) 121, 383-407 (1985). Let GL(A) be the infinite general linear group of a ring A and let B be an \(A\otimes {\mathbb{Q}}\)-bimodule. It is shown that the homology of GL(A) with coefficients the infinite matrices over B is the graded tensor product of the homology of GL(A) with trivial coefficients and the Hochschild homology of \(A\otimes {\mathbb{Q}}\) with coefficients B. The result has applications to stable K-theory and to the algebraic K-theory of simplicial rings. Previous proofs of special cases have used algebraic geometry; this proof uses Lie algebras instead. Reviewer: R.J.Steiner Cited in 1 ReviewCited in 11 Documents MSC: 20G10 Cohomology theory for linear algebraic groups 18F25 Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects) 17B56 Cohomology of Lie (super)algebras 20G35 Linear algebraic groups over adèles and other rings and schemes Keywords:general linear group; graded tensor product; Hochschild homology; stable K-theory; algebraic K-theory PDFBibTeX XMLCite \textit{T. G. Goodwillie}, Ann. Math. (2) 121, 383--407 (1985; Zbl 0566.20021) Full Text: DOI