000 04273nam a22005415i 4500
001 978-3-642-22597-0
003 DE-He213
005 20190213151552.0
007 cr nn 008mamaa
008 111010s2012 gw | s |||| 0|eng d
020 _a9783642225970
_9978-3-642-22597-0
024 7 _a10.1007/978-3-642-22597-0
_2doi
050 4 _aQA252.3
050 4 _aQA387
072 7 _aPBG
_2bicssc
072 7 _aMAT014000
_2bisacsh
072 7 _aPBG
_2thema
082 0 4 _a512.55
_223
082 0 4 _a512.482
_223
100 1 _aBonfiglioli, Andrea.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aTopics in Noncommutative Algebra
_h[electronic resource] :
_bThe Theorem of Campbell, Baker, Hausdorff and Dynkin /
_cby Andrea Bonfiglioli, Roberta Fulci.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2012.
300 _aXXII, 539 p. 5 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2034
505 0 _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.
520 _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.
650 0 _aTopological Groups.
650 0 _aAlgebra.
650 0 _aGlobal differential geometry.
650 1 4 _aTopological Groups, Lie Groups.
_0http://scigraph.springernature.com/things/product-market-codes/M11132
650 2 4 _aHistory of Mathematical Sciences.
_0http://scigraph.springernature.com/things/product-market-codes/M23009
650 2 4 _aNon-associative Rings and Algebras.
_0http://scigraph.springernature.com/things/product-market-codes/M11116
650 2 4 _aDifferential Geometry.
_0http://scigraph.springernature.com/things/product-market-codes/M21022
700 1 _aFulci, Roberta.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642225963
776 0 8 _iPrinted edition:
_z9783642225987
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2034
856 4 0 _uhttps://doi.org/10.1007/978-3-642-22597-0
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c11132
_d11132