Topics in Noncommutative Algebra
Bonfiglioli, Andrea.
Topics in Noncommutative Algebra The Theorem of Campbell, Baker, Hausdorff and Dynkin / [electronic resource] : by Andrea Bonfiglioli, Roberta Fulci. - XXII, 539 p. 5 illus. online resource. - Lecture Notes in Mathematics, 2034 0075-8434 ; . - Lecture Notes in Mathematics, 2034 .
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.
9783642225970
10.1007/978-3-642-22597-0 doi
Topological Groups.
Algebra.
Global differential geometry.
Topological Groups, Lie Groups.
History of Mathematical Sciences.
Non-associative Rings and Algebras.
Differential Geometry.
QA252.3 QA387
512.55 512.482
Topics in Noncommutative Algebra The Theorem of Campbell, Baker, Hausdorff and Dynkin / [electronic resource] : by Andrea Bonfiglioli, Roberta Fulci. - XXII, 539 p. 5 illus. online resource. - Lecture Notes in Mathematics, 2034 0075-8434 ; . - Lecture Notes in Mathematics, 2034 .
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.
9783642225970
10.1007/978-3-642-22597-0 doi
Topological Groups.
Algebra.
Global differential geometry.
Topological Groups, Lie Groups.
History of Mathematical Sciences.
Non-associative Rings and Algebras.
Differential Geometry.
QA252.3 QA387
512.55 512.482