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On the general linear group and Hochschild homology. (English) Zbl 0566.20021

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

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
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