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: Publication Date: 1/30/2014 12:00:00 AM
      ISBN13: 9781470436544, 978-1470436544
      ISBN10: 147043654X

      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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