On a hidden supersymmetry of cosmological billiards

Abstract

The hyperbolic Lie algebras with symmetrizable Cartan matrix are classified, there are 142 of them some of which can be ``superized'' to an almost affine Lie superalgebra. We list all 97 pairs (a hyperbolic Lie algebra $H$, its superized almost affine Lie superalgebra $S(H)$). Several (18 of the total 66) superizable hyperbolic Lie algebras have multiple superizations. The tracks of cosmological billiards corresponding to both terms of these pairs ($H\leftrightarrow S(H)$) are the same since the Weyl chambers of $H$ and of $S(H)$ differ only by a~scale. We also classified ``superizations'' of hyperbolic Lie algebras with non-symmetrizable Cartan matrix. No interpretations of these Lie (super)algebras are known to us.