Overview
- A full historical treatise on the early proofs of the Theorem of Campbell, Baker, Hausdorff and Dynkin is presented here for the first time
- The book is completely self-contained and accessible to all audiences
- The book contains the proofs of all the algebraic prerequisites and can also provide a textbook for topics in non-commutative algebra
- Includes supplementary material: sn.pub/extras
Part of the book series: Lecture Notes in Mathematics (LNM, volume 2034)
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Table of contents (10 chapters)
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Front Matter
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Algebraic Proofs of the Theorem of Campbell, Baker, Hausdorff and Dynkin
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Front Matter
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Proofs of the Algebraic Prerequisites
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Front Matter
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Back Matter
Keywords
About this book
Motivated by the importance of the Campbell, Baker, Hausdorff, Dynkin Theorem in many different branches of Mathematics and Physics (Lie group-Lie algebra theory, linear PDEs, Quantum and Statistical Mechanics, Numerical Analysis, Theoretical Physics, Control Theory, sub-Riemannian Geometry), this monograph is intended to: fully enable readers (graduates or specialists, mathematicians, physicists or applied scientists, acquainted with Algebra or not) to understand and apply the statements and numerous corollaries of the main result, provide a wide spectrum of proofs from the modern literature, comparing different techniques and furnishing a unifying point of view and notation, provide a thorough historical background of the results, together with unknown facts about the effective early contributions by Schur, Poincaré, Pascal, Campbell, Baker, Hausdorff and Dynkin, give an outlook on the applications, especially in Differential Geometry (Lie group theory) and Analysis (PDEs of subelliptic type) and quickly enable the reader, through a description of the state-of-art and open problems, to understand the modern literature concerning a theorem which, though having its roots in the beginning of the 20th century, has not ceased to provide new problems and applications.
The book assumes some undergraduate-level knowledge of algebra and analysis, but apart from that is self-contained. Part II of the monograph is devoted to the proofs of the algebraic background. The monograph may therefore provide a tool for beginners in Algebra.
Authors and Affiliations
Bibliographic Information
Book Title: Topics in Noncommutative Algebra
Book Subtitle: The Theorem of Campbell, Baker, Hausdorff and Dynkin
Authors: Andrea Bonfiglioli, Roberta Fulci
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-642-22597-0
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2012
Softcover ISBN: 978-3-642-22596-3Published: 12 October 2011
eBook ISBN: 978-3-642-22597-0Published: 11 October 2011
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XXII, 539
Number of Illustrations: 5 b/w illustrations
Topics: Topological Groups, Lie Groups, History of Mathematical Sciences, Non-associative Rings and Algebras, Differential Geometry