Topics in Noncommutative Algebra

The Theorem of Campbell, Baker, Hausdorff and Dynkin

  • Andrea Bonfiglioli
  • Roberta Fulci

Part of the Lecture Notes in Mathematics book series (LNM, volume 2034)

Table of contents

  1. Front Matter
    Pages i-xxii
  2. Andrea Bonfiglioli, Roberta Fulci
    Pages 1-45
  3. Algebraic Proofs of the Theorem of Campbell, Baker, Hausdorff and Dynkin

    1. Front Matter
      Pages 47-47
    2. Andrea Bonfiglioli, Roberta Fulci
      Pages 49-114
    3. Andrea Bonfiglioli, Roberta Fulci
      Pages 115-172
    4. Andrea Bonfiglioli, Roberta Fulci
      Pages 173-264
    5. Andrea Bonfiglioli, Roberta Fulci
      Pages 265-369
  4. Proofs of the Algebraic Prerequisites

    1. Front Matter
      Pages 391-391
    2. Andrea Bonfiglioli, Roberta Fulci
      Pages 393-457
    3. Andrea Bonfiglioli, Roberta Fulci
      Pages 459-477
    4. Andrea Bonfiglioli, Roberta Fulci
      Pages 479-499
    5. Andrea Bonfiglioli, Roberta Fulci
      Pages 501-521
  5. Back Matter
    Pages 523-539

About this book

Introduction

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:
1) 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;
2) provide a wide spectrum of proofs from the modern literature, comparing different techniques and furnishing a unifying point of view and notation;
3) 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;
4) give an outlook on the applications, especially in Differential Geometry (Lie group theory) and Analysis (PDEs of subelliptic type);
5) 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.

Keywords

22-XX, 01-XX, 17-XX, 53-XX Flows of vector fields Free Lie algebras Structure theory of Lie groups and Lie algebras The Theorem of Campbell, Baker, Hausdorff & Dynkin

Authors and affiliations

  • Andrea Bonfiglioli
    • 1
  • Roberta Fulci
    • 2
  1. 1.Dipto. MatematicaUniversità di BolognaBolognaItaly
  2. 2., Department of MathematicsUniversity of BolognaBolognaItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-22597-0
  • Copyright Information Springer-Verlag Berlin Heidelberg 2012
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-22596-3
  • Online ISBN 978-3-642-22597-0
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book