On the homology of Lie algebras like $\mathfrak{gl}(\infty,R)$
Oliver Braunling
TL;DR
This paper revisits the homology of the Lie algebra gl(\u221e,R) and offers an alternative method to derive known results, enhancing understanding of its algebraic structure.
Contribution
It provides a new approach to compute the homology of gl( ,R), complementing previous work by Fialowski and Iohara.
Findings
Confirmed the homology results for gl( ,R) using a different method
Demonstrated the versatility of alternative computational techniques in Lie algebra homology
Enhanced theoretical understanding of infinite-dimensional Lie algebra homology
Abstract
We revisit a recent paper of Fialowski and Iohara. They compute the homology of the Lie algebra for an associative unital algebra over a field of characteristic zero. We explain how to obtain essentially the same results by a completely different method.
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