Topics in noncommutative algebra: the theorem of Campbell, Baker, Hausdorff and Dynkin

Motivated by the importance of the Campbell, Baker, Hausdorff, Dynkin Theoremin 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 isintended 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) andquickly enable the reader, through a description of the state-of-art and openproblems, 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. 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 INDICE: 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 LieAlgebras. 9 Formal Power Series in One Indeterminate. 10 Symmetric Algebra.

• ISBN: 978-3-642-22596-3
• Editorial: Springer Berlin Heidelberg
• Encuadernacion: Rústica
• Páginas: 498
• Fecha Publicación: 31/10/2011
• Nº Volúmenes: 1
• Idioma: Inglés