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Classification and Identification of Lie Algebras
Libor Šnobl, Czech Technical University, Prague, Czech Republic, and Pavel Winternitz, Centre de Recherches Mathématiques, Montréal, QC, Canada, and Université de Montréal, QC, Canada
A co-publication of the AMS and Centre de Recherches Mathématiques.

CRM Monograph Series
2014; 306 pp; hardcover
Volume: 33
ISBN-10: 0-8218-4355-9
ISBN-13: 978-0-8218-4355-0
List Price: US$124
Member Price: US$99.20
Order Code: CRMM/33
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The purpose of this book is to serve 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. This includes algorithms accomplishing decomposition into a direct sum, identification of the radical and the Levi decomposition, and the computation of the nilradical and of the Casimir invariants. Examples are given for each algorithm.

For low-dimensional Lie algebras this makes it possible to identify the given Lie algebra completely. The authors provide a representative list of all Lie algebras of dimension less or equal to 6 together with their important properties, including their Casimir invariants. The list is ordered in a way to make identification easy, using only basis independent properties of the Lie algebras. They also describe certain classes of nilpotent and solvable Lie algebras of arbitrary finite dimensions for which complete or partial classification exists and discuss in detail their construction and properties.

The book is based on material that was previously dispersed in journal articles, many of them written by one or both of the authors together with their collaborators. The reader of this book should be familiar with Lie algebra theory at an introductory level.

Titles in this series are co-published with the Centre de Recherches Mathématiques.


Undergraduate students, graduate students, and research mathematicians interested in structure and applications of Lie algebras.


"Summarizing, this book is a highly welcome addition to the bookshelf and will certainly become a valuable and indispensable tool for the practitioner in Lie theory, as it presents in condensed form a huge quantity of information dispersed in the technical literature.

"Click here to view this review in its entirety."

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