The classification of almost affine (hyperbolic) Lie superalgebras

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.

92 pages

References in corpus (5)

• Higher order M theory corrections and the Kac-Moody algebra E10
• Classification of hyperbolic Dynkin diagrams, root lengths and Weyl group orbits
• Hyperbolic Kac Moody Algebras and Einstein Billiards
• Automorphisms and forms of simple infinite-dimensional linearly compact Lie superalgebras
• The Poincare series of the hyperbolic Coxeter groups with finite volume of fundamental domains

Cited by in corpus (5)

• Classification of simple Lie superalgebras in characteristic $2$
• Non-degenerate invariant (super)symmetric bilinear forms on simple Lie (super)algebras
• The Poincare series of the hyperbolic Coxeter groups with finite volume of fundamental domains
• New Constructions of Exceptional Simple Lie Superalgebras with Integer Cartan Matrix in Characteristics 3 and 5 via Tensor Categories
• Defining relations of almost affine (hyperbolic) superalgebras