This is the softcover reprint of the 1975 English translation of the first three chapters of Bourbaki’s Groupes et algebres de Lie. The first chapter describes the theory of Lie algebras, their deviations, representations, and enveloping algebras. Chapter two introduces free Lie algebras in order to discuss the exponential, logarithmic and the Hausdorff series. Chapter three deals with the theory of Lie groups over R and C ultrametric fields.
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3 of 3 people found the following review helpful:
5.0 out of 5 stars
great as references, and..,
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This review is from: Lie Groups and Lie Algebras: Chapters 1-3 (Paperback)
...even better when supplemented by other texts (be wary though, as the notation of Bourbaki is not universally accepted).
I'd buy them simply for their sparkling clarity and careful attention to rigour (esp. Commalg, Lie theory and integration). These are wonderfully crafted, masterful expositions, and should not, by any means, be overlooked by the (aspiring) pure mathematician. Cheers, A.
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Inside This Book
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First Sentence:
Let M be a unitary module over K with a bilinear mapping (x, y) xy of M x M into M. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
analytic linear representation, integral subgroup, largest nilpotency ideal, subgroup germ, law chunk, polynormed space, normable algebra, enveloping bigebra, bigebra structure, bigebra morphism, normable space, topological supplement, homogeneous symmetric tensors, cogebra structure, supplementary subalgebra, real filtration, mod deg, subalgebra tangent, central filtration, analytic manifold structure, infinitely small transformation, symmetric open neighbourhood, largest nilpotent ideal, canonical differential form, integral filtration Key Phrases - Capitalized Phrases (CAPs): (learn more)
General Topology, Spectral Theories, Lie Z-algebra, Poincaré-Birkhoff-Witt Theorem, Set Theory New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Let M be a unitary module over K with a bilinear mapping (x, y) xy of M x M into M. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
analytic linear representation, integral subgroup, largest nilpotency ideal, subgroup germ, law chunk, polynormed space, normable algebra, enveloping bigebra, bigebra structure, bigebra morphism, normable space, topological supplement, homogeneous symmetric tensors, cogebra structure, supplementary subalgebra, real filtration, mod deg, subalgebra tangent, central filtration, analytic manifold structure, infinitely small transformation, symmetric open neighbourhood, largest nilpotent ideal, canonical differential form, integral filtration Key Phrases - Capitalized Phrases (CAPs): (learn more)
General Topology, Spectral Theories, Lie Z-algebra, Poincaré-Birkhoff-Witt Theorem, Set Theory New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 2
books:
23
books
cite this book:
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- Lie Algebras (Dover Books on Mathematics) by Nathan Jacobson on page 43
- Commutative Algebra (Elements of Mathematics) by Nicolas Bourbaki in Back Matter
- Math Through the Ages: A Gentle History for Teachers and Others, Expanded Edition (Mathematical Association of America Textbooks) by William P. Berlinghoff on page 55, page 56, and Index
- The Foundations of Mathematics in the Theory of Sets (Encyclopedia of Mathematics and its Applications) by John P. Mayberry on page 99, and Back Matter
- Gödel's Theorem in Focus (Philosophers in Focus) by S.G. Shanker on page 251, and page 252
- Mathematics: The Loss of Certainty (Galaxy Books) by Morris Kline on page 320
- Handbook of Algebra, Volume 3 by Sahra Sedigh on page 767
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