Nilpotent Lie Algebras / Edition 1

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This volume is devoted to the theory of nilpotent Lie algebras and their applications. Nilpotent Lie algebras have played an important role over the last years both in the domain of algebra, considering its role in the classification problems of Lie algebras, and in the domain of differential geometry. Among the topics discussed here are the following: cohomology theory of Lie algebras, deformations and contractions, the algebraic variety of the laws of Lie algebras, the variety of nilpotent laws, and characteristically nilpotent Lie algebras in nilmanifolds.
Audience: This book is intended for graduate students specialising in algebra, differential geometry and in theoretical physics and for researchers in mathematics and in theoretical physics.

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Product Details

  • ISBN-13: 9789048146710
  • Publisher: Springer Netherlands
  • Publication date: 12/10/2010
  • Series: Mathematics and Its Applications (closed) Series, #361
  • Edition description: Softcover reprint of hardcover 1st ed. 1996
  • Edition number: 1
  • Pages: 336
  • Product dimensions: 6.14 (w) x 9.21 (h) x 0.74 (d)

Table of Contents

Preface. 1. Lie Algebras. Generalities. 2. Some Classes of Nilpotent Lie Algebras. 3. Cohomology of Lie Algebras. 4. Cohomology of Some Nilpotent Lie Algebras. 5. The Algebraic Variety of the Laws of Lie Algebras. 6. Variety of Nilpotent Lie Algebras. 7. Characteristically Nilpotent Lie Algebras. 8. Applications to Differential Geometry. The Nilmanifolds. Bibliography. Index.

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  • Anonymous

    Posted May 31, 2002

    Good intention. Bad execution

    This book intends to be a comprehensive introduction to the study of nilpotent Lie algebras over a field of characteristic zero. The main aspects dealt in the text are the analysis of the variety of nilpotent Lie algebra laws, with a study of the irreducible components, the cohomology of filiform algebras and standard nilalgebras and the study of characteristically nilpotent Lie algebras. The final chapter also presents some applications to differential geometry. Although the idea is good, the execution and organization of the book is far from being optimal. Some concepts are repeatedly defined, and the notation used is not the same for the whole book, but differs from chapter to chapter. The book also presents a great number of misprints and lists of Lie algebras which have errors. The bibliography is not well structured, and some important references are missing. Resuming, a text exclusively for experts in the area, since the great number of mistakes will surely lead students to erroneous interpretations of the text.

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