The classification of almost affine (hyperbolic) Lie superalgebras

TL;DR

This paper classifies almost affine (hyperbolic) Lie superalgebras, a special class of infinite-dimensional algebras characterized by their Cartan matrices, correcting previous classification errors and providing comprehensive lists.

Contribution

It provides a corrected and complete classification of almost affine Lie superalgebras over complex numbers, including new lists and clarifications of earlier claims.

Findings

Complete list of almost affine Lie superalgebras over complex numbers.

Correction of two earlier classification errors.

Availability of a comprehensive list of almost affine Lie algebras.

Abstract

We say that an indecomposable Cartan matrix A with entries in the ground field of characteristic 0 is almost affine if the Lie sub(super)algebra determined by it is not finite dimensional or affine but the Lie (super)algebra determined by any submatrix of A, obtained by striking out any row and any column intersecting on the main diagonal, is the sum of finite dimensional or affine Lie (super)algebras. A Lie (super)algebra with Cartan matrix is said to be almost affine if it is not finite dimensional or affine, and all of its Cartan matrices are almost affine. We list all almost affine Lie superalgebras over complex numbers correcting two earlier claims of classification and make available the list of almost affine Lie algebras obtained by Li Wang Lai.