Topics in Noncommutative Algebra

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Oktober 2011



Motivated by the importance of the result usually referred to as the Theorem of Campbell, Baker, Hausdorff and Dynkin 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 modern literature, comparing the 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) predict 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 on 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 is self-contained (apart from the use of some undergraduate algebra and analysis). Part II of the monograph is devoted to the proofs of the algebraic background: It is left to the reader to decide which proofs to consult or to skip. The monograph may therefore provide a valuable tool for beginners in algebra.


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.
EAN: 9783642225963
ISBN: 3642225969
Untertitel: The Theorem of Campbell, Baker, Hausdorff and Dynkin. 'Lecture Notes in Mathematics'. Edition. 3 schwarz-weiße Abbildungen. Book. Sprache: Englisch.
Verlag: Springer-Verlag GmbH
Erscheinungsdatum: Oktober 2011
Seitenanzahl: XXII
Format: kartoniert
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