## Abstract

The concept of automorphic Lie algebras arises in the context of reduction groups introduced in the early 1980s in the field of integrable systems. automorphic Lie algebras are obtained by imposing a discrete group symmetry on a current algebra of KricheverNovikov type. Past work shows remarkable uniformity between algebras associated to different reduction groups. For example, if the base Lie algebra is sl_{2}(ℂ) and the poles of the automorphic Lie algebra are restricted to an exceptional orbit of the symmetry group, changing the reduction group does not affect the Lie algebra structure. In this research we fix the reduction group to be the dihedral group and vary the orbit of poles as well as the group action on the base Lie algebra. We find a uniform description of automorphic Lie algebras with dihedral symmetry, valid for poles at exceptional and generic orbits.

Original language | English |
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Article number | 365201 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 47 |

Issue number | 36 |

DOIs | |

Publication status | Published - 12 Sept 2014 |

## Keywords

- automorphic Lie algebras
- classical invariant theory
- dihedral symmetry

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Modelling and Simulation
- Mathematical Physics
- General Physics and Astronomy