Locally loop algebras and locally affine Lie algebras

In this study, we investigate a new class of Lie algebras, i.e., tame locally extended affine Lie algebras of nullity 1, which are an infinite-rank analog of affine Lie algebras. This type of algebra is called a locally affine Lie algebra. A certain ideal of a locally affine Lie algebra, called a core, is a universal extension of a local version of a loop algebra, which is called a locally loop algebra. We classify locally loop algebras and locally affine Lie algebras.