Homology of the Lie algebra $\mathfrak{gl}(\infty ,R)$

Abstract

In this note we compute the homology of the Lie algebra $\mathfrak{gl}(\infty ,R)$ where $R$ is an associative unital $k$-algebra which is used in higher dimensional soliton theory. When $k$ is a field of characteristic $0$, our result justifies an old result of Feigin and Tsygan appeared in 1983. The special case when $R=k$ is the complex number field $\mathbb{C}$ appeared first in soliton theory.

arXiv commentTo appear in Ann. Sc. Norm. Super. Cl. Sci. (5)