### Abstract

An extended Vogan diagram is an extended Dynkin diagram with a diagram involution, such that the vertices fixed by the involution can be painted or unpainted. Every extended Vogan diagram represents an almost compact real form of some affine Kac-Moody Lie algebra. Two diagrams may represent isomorphic algebras, and in this case we say that the diagrams are equivalent. In this paper, we classify the equivalence classes of extended Vogan diagrams, and provide a complete list of all diagrams within each class. It gives a combinatorial classification of the isomorphic classes of almost compact real forms of the affine Kac-Moody Lie algebras.

Original language | English |
---|---|

Pages (from-to) | 112-147 |

Number of pages | 36 |

Journal | Journal of Algebra |

Volume | 301 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2006 Jul 1 |

### Fingerprint

### Keywords

- Almost compact real form
- Extended Vogan diagram
- Kac-Moody Lie algebra

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*Journal of Algebra*,

*301*(1), 112-147. https://doi.org/10.1016/j.jalgebra.2005.12.022

**Extended Vogan diagrams.** / Chuah, Meng Kiat; Hu, Chu-Chin.

Research output: Contribution to journal › Article

*Journal of Algebra*, vol. 301, no. 1, pp. 112-147. https://doi.org/10.1016/j.jalgebra.2005.12.022

}

TY - JOUR

T1 - Extended Vogan diagrams

AU - Chuah, Meng Kiat

AU - Hu, Chu-Chin

PY - 2006/7/1

Y1 - 2006/7/1

N2 - An extended Vogan diagram is an extended Dynkin diagram with a diagram involution, such that the vertices fixed by the involution can be painted or unpainted. Every extended Vogan diagram represents an almost compact real form of some affine Kac-Moody Lie algebra. Two diagrams may represent isomorphic algebras, and in this case we say that the diagrams are equivalent. In this paper, we classify the equivalence classes of extended Vogan diagrams, and provide a complete list of all diagrams within each class. It gives a combinatorial classification of the isomorphic classes of almost compact real forms of the affine Kac-Moody Lie algebras.

AB - An extended Vogan diagram is an extended Dynkin diagram with a diagram involution, such that the vertices fixed by the involution can be painted or unpainted. Every extended Vogan diagram represents an almost compact real form of some affine Kac-Moody Lie algebra. Two diagrams may represent isomorphic algebras, and in this case we say that the diagrams are equivalent. In this paper, we classify the equivalence classes of extended Vogan diagrams, and provide a complete list of all diagrams within each class. It gives a combinatorial classification of the isomorphic classes of almost compact real forms of the affine Kac-Moody Lie algebras.

KW - Almost compact real form

KW - Extended Vogan diagram

KW - Kac-Moody Lie algebra

UR - http://www.scopus.com/inward/record.url?scp=33646713685&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33646713685&partnerID=8YFLogxK

U2 - 10.1016/j.jalgebra.2005.12.022

DO - 10.1016/j.jalgebra.2005.12.022

M3 - Article

AN - SCOPUS:33646713685

VL - 301

SP - 112

EP - 147

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

IS - 1

ER -