Topics in noncommutative algebra : the theorem of Campbell, Baker, Hausdorff and Dynkin
 Author/Creator
 Bonfiglioli, Andrea.
 Language
 English.
 Imprint
 Heidelberg ; New York : SpringerVerlag, 2012.
 Physical description
 xxii, 539 p. : ill. ; 24 cm.
 Series
 Lecture notes in mathematics (SpringerVerlag) 2034.
Access
Available online
 www.springerlink.com
 dx.doi.org SpringerLink

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QA3 .L28 V.2034

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QA3 .L28 V.2034
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Contributors
 Contributor
 Fulci, Roberta.
Contents/Summary
 Bibliography
 Includes bibliographical references (p. 529536) and index.
 Contents

 1 Historical Overview. Part I Algebraic Proofs of the CBHD Theorem. 2 Background Algebra. 3 The Main Proof of the CBHD Theorem. 4 Some 'Short' Proofs of the CBHD Theorem. 5 Convergence and Associativity for the CBHD Theorem. 6 CBHD, PBW and the Free Lie Algebras. Part II Proofs of the Algebraic Prerequisites. 7 Proofs of the Algebraic Prerequisites. 8 Construction of Free Lie Algebras. 9 Formal Power Series in One Indeterminate. 10 Symmetric Algebra.
 (source: Nielsen Book Data)
 Publisher's Summary
 Motivated by the importance of the Campbell, Baker, Hausdorff, Dynkin Theorem in many different branches of Mathematics and Physics (Lie groupLie algebra theory, linear PDEs, Quantum and Statistical Mechanics, Numerical Analysis, Theoretical Physics, Control Theory, subRiemannian 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, Poincare, 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 stateofart 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 undergraduatelevel knowledge of algebra and analysis, but apart from that is selfcontained. 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.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2012
 Responsibility
 Andrea Bonfiglioli, Roberta Fulci.
 Series
 Lecture notes in mathematics ; 2034
 ISBN
 9783642225963
 3642225969
 9783642225970
 3642225977