Extended Vogan diagrams

• Published in: Journal of algebra Vol. 301; no. 1; pp. 112 - 147
• Main Authors: Chuah, Meng-Kiat, Hu, Chu-Chin
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.07.2006
• Subjects: Almost compact real form; Extended Vogan diagram; Kac–Moody Lie algebra; Almost compact real form; Kac–Moody Lie algebra; Extended Vogan diagram
• ISSN: 0021-8693; 1090-266X
• DOI: 10.1016/j.jalgebra.2005.12.022

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.