05039nam 22008175 450 99646651330331620200630025759.03-642-22597-710.1007/978-3-642-22597-0(CKB)2550000000056692(SSID)ssj0000611021(PQKBManifestationID)11357381(PQKBTitleCode)TC0000611021(PQKBWorkID)10644631(PQKB)11417785(DE-He213)978-3-642-22597-0(MiAaPQ)EBC3067409(PPN)163736294(EXLCZ)99255000000005669220111010d2012 u| 0engurnn|008mamaatxtccrTopics in Noncommutative Algebra[electronic resource] The Theorem of Campbell, Baker, Hausdorff and Dynkin /by Andrea Bonfiglioli, Roberta Fulci1st ed. 2012.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2012.1 online resource (XXII, 539 p. 5 illus.) Lecture Notes in Mathematics,0075-8434 ;2034Bibliographic Level Mode of Issuance: Monograph3-642-22596-9 Includes bibliographical references and index.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.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.Lecture Notes in Mathematics,0075-8434 ;2034Topological groupsLie groupsMathematicsHistoryNonassociative ringsRings (Algebra)Differential geometryTopological Groups, Lie Groupshttps://scigraph.springernature.com/ontologies/product-market-codes/M11132History of Mathematical Scienceshttps://scigraph.springernature.com/ontologies/product-market-codes/M23009Non-associative Rings and Algebrashttps://scigraph.springernature.com/ontologies/product-market-codes/M11116Differential Geometryhttps://scigraph.springernature.com/ontologies/product-market-codes/M21022Topological 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.512.55512.482510sdnbMAT 173fstubMAT 220fstubMAT 530fstubSI 850rvkBonfiglioli Andreaauthttp://id.loc.gov/vocabulary/relators/aut327207Fulci Robertaauthttp://id.loc.gov/vocabulary/relators/autBOOK996466513303316Topics in Noncommutative Algebra2831261UNISA