Topics in Noncommutative Algebra : The Theorem of Campbell, Baker, Hausdorff and Dynkin / by Andrea Bonfiglioli, Roberta Fulci.

Format:

Book

Author/Creator:

Bonfiglioli, Andrea, author.

Fulci, Roberta, author.

Contributor:

SpringerLink (Online service)

Series:

Lecture Notes in Mathematics, 0075-8434 ; 2034.

Lecture Notes in Mathematics, 0075-8434 ; 2034

Language:

English

Subjects (All):

Topological groups.

Algebra.

Global differential geometry.

Topological Groups, Lie Groups.

History of Mathematical Sciences.

Non-associative Rings and Algebras.

Differential Geometry.

Local Subjects:

Topological Groups, Lie Groups.

History of Mathematical Sciences.

Non-associative Rings and Algebras.

Differential Geometry.

Physical Description:

1 online resource (XXII, 539 pages 5 illustrations).

Contained In:

Springer eBooks

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg, 2012.

System Details:

text file PDF

Summary:

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.

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.

Other Format:

Printed edition:

ISBN:

9783642225970

Access Restriction:

Restricted for use by site license.