LEADER 05039nam 22008175 450 001 996466513303316 005 20200630025759.0 010 $a3-642-22597-7 024 7 $a10.1007/978-3-642-22597-0 035 $a(CKB)2550000000056692 035 $a(SSID)ssj0000611021 035 $a(PQKBManifestationID)11357381 035 $a(PQKBTitleCode)TC0000611021 035 $a(PQKBWorkID)10644631 035 $a(PQKB)11417785 035 $a(DE-He213)978-3-642-22597-0 035 $a(MiAaPQ)EBC3067409 035 $a(PPN)163736294 035 $a(EXLCZ)992550000000056692 100 $a20111010d2012 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aTopics in Noncommutative Algebra$b[electronic resource] $eThe Theorem of Campbell, Baker, Hausdorff and Dynkin /$fby Andrea Bonfiglioli, Roberta Fulci 205 $a1st ed. 2012. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2012. 215 $a1 online resource (XXII, 539 p. 5 illus.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v2034 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-642-22596-9 320 $aIncludes bibliographical references and index. 327 $a1 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. 330 $aMotivated by the importance of the Campbell, Baker, Hausdorff, Dynkin Theorem in many different branches of Mathematics and Physics (Lie group-Lie algebra theory, linear PDEs, Quantum and Statistical Mechanics, Numerical Analysis, Theoretical Physics, Control Theory, sub-Riemannian Geometry), this monograph is intended to: 1) fully enable readers (graduates or specialists, mathematicians, physicists or applied scientists, acquainted with Algebra or not) to understand and apply the statements and numerous corollaries of the main result; 2) provide a wide spectrum of proofs from the modern literature, comparing different techniques and furnishing a unifying point of view and notation; 3) provide a thorough historical background of the results, together with unknown facts about the effective early contributions by Schur, Poincaré, Pascal, Campbell, Baker, Hausdorff and Dynkin; 4) give an outlook on the applications, especially in Differential Geometry (Lie group theory) and Analysis (PDEs of subelliptic type); 5) quickly enable the reader, through a description of the state-of-art and open problems, to understand the modern literature concerning a theorem which, though having its roots in the beginning of the 20th century, has not ceased to provide new problems and applications. The book assumes some undergraduate-level knowledge of algebra and analysis, but apart from that is self-contained. Part II of the monograph is devoted to the proofs of the algebraic background. The monograph may therefore provide a tool for beginners in Algebra. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v2034 606 $aTopological groups 606 $aLie groups 606 $aMathematics 606 $aHistory 606 $aNonassociative rings 606 $aRings (Algebra) 606 $aDifferential geometry 606 $aTopological Groups, Lie Groups$3https://scigraph.springernature.com/ontologies/product-market-codes/M11132 606 $aHistory of Mathematical Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/M23009 606 $aNon-associative Rings and Algebras$3https://scigraph.springernature.com/ontologies/product-market-codes/M11116 606 $aDifferential Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21022 615 0$aTopological groups. 615 0$aLie groups. 615 0$aMathematics. 615 0$aHistory. 615 0$aNonassociative rings. 615 0$aRings (Algebra). 615 0$aDifferential geometry. 615 14$aTopological Groups, Lie Groups. 615 24$aHistory of Mathematical Sciences. 615 24$aNon-associative Rings and Algebras. 615 24$aDifferential Geometry. 676 $a512.55 676 $a512.482 686 $a510$2sdnb 686 $aMAT 173f$2stub 686 $aMAT 220f$2stub 686 $aMAT 530f$2stub 686 $aSI 850$2rvk 700 $aBonfiglioli$b Andrea$4aut$4http://id.loc.gov/vocabulary/relators/aut$0327207 702 $aFulci$b Roberta$4aut$4http://id.loc.gov/vocabulary/relators/aut 906 $aBOOK 912 $a996466513303316 996 $aTopics in Noncommutative Algebra$92831261 997 $aUNISA