A note on the Lie algebra \({\mathfrak g}(m\infty)\) (Q1118022)

The author first recalls the principal realization \({\mathfrak g}(\infty)\) for the infinite rank affine Lie algebras \({\mathfrak g}_{\infty}\) (\({\mathfrak g}=a,b,c,d)\). Then the Lie algebras \({\mathfrak g}(m\infty)\) are introduced. Using the isomorphism \({\mathfrak gl}(m\infty)\cong {\mathfrak gl}(\infty)\), the author gives the realizations \({\mathfrak g}(m\infty)\) of the algebras \({\mathfrak g}_{\infty}\).