${\mathfrak{sl}}_2$ triples whose nilpositive elements are in a space which is spanned by the real root vectors in rank 2 symmetric hyperbolic Kac-Moody Lie algebras

Abstract

In analogy to the theory of nilpotent orbit in finite-dimensional semisimple Lie algebras, it is known that the principal ${\mathfrak{sl}}_2$ subalgebras can be constructed in hyperbolic Kac-Moody Lie algebras. We obtained a series of ${\mathfrak{sl}}_2$ subalgebras in rank 2 symmetric hyperbolic Kac-Moody Lie algebras by extending the aforementioned construction. We present this result and also discuss ${\mathfrak{sl}}_2$ modules obtained by the action of the ${\mathfrak{sl}}_2$ subalgebras on the original Lie algebras.

21 pages

References in corpus (1)

• A class of Lorentzian Kac-Moody algebras