Equivalence classes of Vogan diagrams

Meng Kiat Chuah, Chu-Chin Hu

Research output: Contribution to journalArticle

16 Citations (Scopus)

Abstract

A Vogan diagram is a Dynkin diagram with an involution, and the vertices fixed by the involution may be painted. They represent real simple Lie algebras, and two diagrams are said to be equivalent if they represent the same Lie algebra. In this article we classify the equivalence classes of all Vogan diagrams. In doing so, we find that the underlying Dynkin diagrams have certain properties in graph painting. We show that this combinatorial property provides an easy classification for most of the simply-laced Dynkin diagrams.

Original languageEnglish
Pages (from-to)22-37
Number of pages16
JournalJournal of Algebra
Volume279
Issue number1
DOIs
Publication statusPublished - 2004 Sep 1

Keywords

  • Dynkin diagram
  • Graph painting
  • Simple Lie algebra
  • Vogan diagram

ASJC Scopus subject areas

  • Algebra and Number Theory

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