Regular subalgebras of affine Kac-Moody algebras

Abstract

We classify regular subalgebras of affine Kac-Moody algebras in terms of their root systems. In the process, we establish that a root system of a subalgebra is always an intersection of the root system of the algebra with a sublattice of its root lattice. We also discuss applications to investigations of regular subalgebras of hyperbolic Kac-Moody algebras and conformally invariant subalgebras of affine Kac-Moody algebras.

arXiv commentTo appear in Journal of Physics A

References in corpus (3)

• Reflection subgroups of Euclidean reflection groups
• Maximal rank root subsystems of hyperbolic root systems
• Conformal Covariance Subalgebras

Cited by in corpus (6)

• Recursive algorithm and branching for nonmaximal embeddings
• Hyperbolic subalgebras of hyperbolic Kac-Moody algebras
• $\pi$-systems and the embedding problem for rank $2$ Kac-Moody Lie algebras
• Maximal root subsystems of affine reflection systems and duality
• Borel-de Siebenthal theory for affine reflection systems
• Reflection subgroups of odd-angled Coxeter groups