Topics in Noncommutative Algebra: The Theorem of Campbell, Baker, Hausdorff and Dynkin - Couverture souple

Bonfiglioli, Andrea; Fulci, Roberta

Couverture souple

ISBN 10 : 3642225969 ISBN 13 : 9783642225963

Editeur : Springer, 2011

Synopsis

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: 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, provide a wide spectrum of proofs from the modern literature, comparing different techniques and furnishing a unifying point of view and notation, 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, give an outlook on the applications, especially in Differential Geometry (Lie group theory) and Analysis (PDEs of subelliptic type) and 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.

A propos du livre

À propos de l'auteur

1) ERMANNO LANCONELLI: --Education and Undergraduate Studies: Dec. 1966, Universita' di Bologna (Mathematics). Career/Employment: 1975-present: Full Professor of Mathematical Analysis at Dipartimento di Matematica, Universita' di Bologna (Italy); Member of the "Accademia dell'Istituto di Bologna" and of the "Accademia delle Scienze, Lettere ed Arti di Modena". 1968-1975: Theaching Assistant at Istituto di Matematica, Universita' di Bologna. --Academic activity: Director of the Istituto di Matematica di Bologna(1978/80), Director of the Undergraduate Mathematics Program, University of Bologna (1990/1999, 2000-2002, 2006-present) Director of PHD program, University of Bologna (1986/91, 1997/2000) --INVITATIONS: -University of Minnesota, Minneapolis (USA) -University of Purdue, West La Fayette, Indiana (USA) -Temple University, Philadelphia, Pennsylvania (USA) -Rutgers University, New Brunswick, New Jersey (USA) -University of Bern, Switzerland -- Specialization main fields: Partial Differential Equations, Potential Theory --CURRENT RESEARCH INTEREST: Second order linear and nonlinear partial differential equations with non- negative characteristic form and application to complex geometry and diffusion processes. Potential Theory and Harmonic Analysis in sub-riemannian settings. Real analysis and geometric methods. --EDITORIAL BOARD: Nonlinear Differential Equations and Applications, Birkhauser. --PUBLICATIONS: More than 70 papers in refereed journals. 2) UGUZZONI FRANCESCO: --Education and Undergraduate Studies: Dec. 1994, Universita' di Bologna (Mathematics) Career/Employment: February 2000: Ph.D. in Mathematical Analysis at Dipartimento di Matematica, Universita' di Bologna (Italy). October 1998: Assistant Professor at Dipartimento di Matematica, Universita' di Bologna. --CURRENT RESEARCH INTEREST: Second order linear and nonlinear partial differential equations with non- negative characteristic form and applications. Harmonic Analysis in sub- riemannian settings. --PUBLICATIONS: About 30 papers in refereed journals. 3) ANDREA BONFIGLIOLI: --Education and Undergraduate Studies: July 1998, Universita' di Bologna (Mathematics) --Career/Employment: March 2002: Ph.D. in Mathematical Analysis at Dipartimento di Matematica, Universita' di Bologna (Italy). November 2006: Assistant Professor at Dipartimento di Matematica, Universita' di Bologna. --CURRENT RESEARCH INTEREST: Second order linear partial differential equations with non-negative characteristic form and applications. Potential Theory in stratified Lie groups. --PUBLICATIONS: About 20 papers in refereed journals.

À propos de la quatrième de couverture

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.

Détails de l'édition

• Éditeur: Springer
• Date d'édition: 2011
• Langue: anglais
• ISBN 10: 3642225969
• ISBN 13: 9783642225963
• Reliure: Broché
• Nombre de pages: 536
• Coordonnées du fabricant: ProductSafety@springernature.com; ProductSafety@springernature.com; ; Europaplatz 3; Heidelberg; 69115; Allemagne