On Lie algebras of generalized Jacobi matrices

Abstract

In this lecutre note, we consider infinite dimensional Lie algebras of generalized Jacobi matrices $\mathfrak{g}J(k)$ and ${\mathfrak{gl}}_{\infty }(k)$, which are important in soliton theory, and their orthogonal and symplectic subalgebras. In particular, we construct the homology ring of the Lie algebra $\mathfrak{g}J(k)$ and of the orthogonal and symplectic subalgebras.

To appear in Banach Center Publications