Regular subalgebras of affine Kac–Moody algebras

Felikson, Anna; Retakh, Alexander; Tumarkin, Pavel

doi:10.1088/1751-8113/41/36/365204

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Journal article

Regular subalgebras of affine Kac–Moody algebras

Felikson, Anna Independent University of Moscow, Russia - Department of Mathematics, University of Fribourg, Switzerland
Retakh, Alexander Department of Mathematics, Stony Brook University, USA
Tumarkin, Pavel Independent University of Moscow, Russia - Department of Mathematics, Michigan State University, East Lansing, USA

30.07.2008

Published in:

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

English 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.

Faculty

Faculté des sciences et de médecine

Department

Département de Mathématiques

Language