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Classification and Identification of Lie Algebras (Paperback)
Loot Price: R3,323
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Classification and Identification of Lie Algebras (Paperback)
Series: CRM Monograph Series
Expected to ship within 12 - 19 working days
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A co-publication of the AMS and Centre de Recherches
Mathématiques. 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.
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