Description

Book Synopsis
Serves as a tool for researchers and practitioners who apply Lie algebras and Lie groups to solve problems arising in science and engineering. The authors address the problem of expressing a Lie algebra obtained in some arbitrary basis in a more suitable basis in which all essential features of the Lie algebra are directly visible.

Table of Contents
  • Title page
  • Contents
  • Preface
  • Acknowledgments
  • 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
  • Bibliography
  • Index

Classification and Identification of Lie Algebras

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A Paperback by Libor Nobl, Pavel Winternitz

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    View other formats and editions of Classification and Identification of Lie Algebras by Libor Nobl

    Publisher: MP-AMM American Mathematical
    Publication Date: 1/30/2014 12:00:00 AM
    ISBN13: 9781470436544, 978-1470436544
    ISBN10: 147043654X
    Also in:
    Algebraic geometry Mathematical / Computational / Theoretical physics

    Description

    Book Synopsis
    Serves as a tool for researchers and practitioners who apply Lie algebras and Lie groups to solve problems arising in science and engineering. The authors address the problem of expressing a Lie algebra obtained in some arbitrary basis in a more suitable basis in which all essential features of the Lie algebra are directly visible.

    Table of Contents
    • Title page
    • Contents
    • Preface
    • Acknowledgments
    • 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
    • Bibliography
    • Index

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