On the homology of Lie algebras like $\mathfrak{gl}(\infty, R)$

We revisit a recent paper of Fialowski and Iohara. They compute the homology of the Lie algebra $\mathfrak{gl}(\infty, R)$ for $R$ an associative unital algebra over a field of characteristic zero. We explain how to obtain essentially the same results by a completely different method.

Keywords

infinite matrix algebra, ring-level delooping

2010 Mathematics Subject Classification

20J05

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The author was supported by DFG GK1821 “Cohomological Methods in Geometry” and a Junior Fellowship at the Freiburg Institute for Advanced Studies (FRIAS).

Received 15 March 2018

Received revised 20 November 2018

Accepted 20 November 2018

Published 13 February 2019