Faculté des sciences

Regular subalgebras of affine Kac–Moody algebras

Felikson, Anna ; Retakh, Alexander ; Tumarkin, Pavel

In: Journal of Physics A, 2008, vol. 41, no. 36, p. 365204

We classify regular subalgebras of 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... Plus

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    Summary
    We classify regular subalgebras of 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. In particular, we provide explicit formulae for determining all Virasoro charges in coset constructions that involve regular subalgebras.