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Classification and Identification of Lie Algebras
About this Title
Libor Šnobl, Czech Technical University, Prague, Czech Republic and Pavel Winternitz, Centre de Recherches Mathématiques, Montréal, QC, Canada
Publication: CRM Monograph Series
Publication Year:
2014; Volume 33
ISBNs: 978-1-4704-3654-4 (print); 978-1-4704-1472-6 (online)
DOI: https://doi.org/10.1090/crmm/033
MathSciNet review: MR3184730
MSC: Primary 17-02; Secondary 17Bxx, 37J15, 70G65, 81R30
Table of Contents
Front/Back Matter
Chapters
- Part 1. General theory
- Introduction and motivation
- Basic concepts
- Invariants of the coadjoint representation of a Lie algebra
- Part 2. Recognition of a Lie algebra given by its structure constants
- Identification of Lie algebras through the use of invariants
- Decomposition into a direct sum
- Levi decomposition. Identification of the radical and Levi factor
- The nilradical of a Lie algebra
- Part 3. Nilpotent, solvable and Levi decomposable Lie algebras
- Nilpotent Lie algebras
- Solvable Lie algebras and their nilradicals
- Solvable Lie algebras with abelian nilradicals
- Solvable Lie algebras with Heisenberg nilradical
- Solvable Lie algebras with Borel nilradicals
- Solvable Lie algebras with filiform and quasifiliform nilradicals
- Levi decomposable algebras
- Part 4. Low-dimensional Lie algebras
- Structure of the lists of low-dimensional Lie algebras
- Lie algebras up to dimension 3
- Four-dimensional Lie algebras
- Five-dimensional Lie algebras
- Six-dimensional Lie algebras