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

• Autore: Bonfiglioli Andrea
• Pubblicazione: Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2012
• Edizione: 1st ed. 2012.
• Descrizione fisica: 1 online resource (XXII, 539 p. 5 illus.)
• Disciplina: 512.55; 512.482
• Soggetto topico: Topological groups; Lie groups; Mathematics; History; Nonassociative rings; Rings (Algebra); Differential geometry; Topological Groups, Lie Groups; History of Mathematical Sciences; Non-associative Rings and Algebras; Differential Geometry
• Classificazione: 510; MAT 173f; MAT 220f; MAT 530f; SI 850
• Persona (resp. second.): FulciRoberta
• Note generali: Bibliographic Level Mode of Issuance: Monograph
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: 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.
• Sommario/riassunto: 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.
• Titolo autorizzato: Topics in Noncommutative Algebra
• ISBN: 3-642-22597-7
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910484917103321
• Lo trovi qui: Univ. Federico II
• Serie: Lecture Notes in Mathematics, . 0075-8434 ; ; 2034