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Autore: | Bonfiglioli Andrea |

Titolo: | Topics in Noncommutative Algebra [[electronic resource] ] : The Theorem of Campbell, Baker, Hausdorff and Dynkin / / by Andrea Bonfiglioli, Roberta Fulci |

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 |

Opac: | Controlla la disponibilità qui |

Serie:
Lecture Notes in Mathematics, . 0075-8434 ; ; 2034