Minimal Representations of Lie Algebras With Non-Trivial Levi\n Decomposition

2017/03/15 by Ryad Ghanam, Ghanam, Ryad, Manoj Lamichhane +3
Chemistry · Materials Science · Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Magnetism in coordination complexes #Representation Theory (math.RT) #Synthesis and Properties of Aromatic Compounds

paper · pdf · doi:10.48550/arxiv.1703.05453

openalex publication_date 2017/03/15 · openalex created_date 2022/09/27 · openalex updated_date 2026/07/28

Abstract

We obtain minimal dimension matrix representations for each of the Lie\nalgebras of dimension five, six, seven, and eight obtained by Turkowski that\nhave a non-trivial Levi decomposition. The Key technique involves using\nsubspace associated to a particular representation of semi-simple Lie algebra\nto help in the construction of the radical in the putative Levi decomposition.\n

Related

• Minimal matrix representations of five-dimensional Lie algebras
• Invariants of the coadjoint representation of Lie algebras in dimension n≤ 8
• The Levi Decomposition of a Graded Lie Algebra
• Classification of minimal representations of real simple Lie groups
• Faithful Representations of Minimal Dimension of 6-dimensional nilpotent Lie algebras