The Lie Theory Of Connected Pro Lie Groups

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The Lie Theory Of Connected Pro Lie Groups

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Author : Karl Heinrich Hofmann
language : en
Publisher: European Mathematical Society
Release Date : 2007

The Lie Theory Of Connected Pro Lie Groups written by Karl Heinrich Hofmann and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.

Lie groups were introduced in 1870 by the Norwegian mathematician Sophus Lie. A century later Jean Dieudonne quipped that Lie groups had moved to the center of mathematics and that one cannot undertake anything without them. If a complete topological group $G$ can be approximated by Lie groups in the sense that every identity neighborhood $U$ of $G$ contains a normal subgroup $N$ such that $G/N$ is a Lie group, then it is called a pro-Lie group. Every locally compact connected topological group and every compact group is a pro-Lie group. While the class of locally compact groups is not closed under the formation of arbitrary products, the class of pro-Lie groups is. For half a century, locally compact pro-Lie groups have drifted through the literature, yet this is the first book which systematically treats the Lie and structure theory of pro-Lie groups irrespective of local compactness. This study fits very well into the current trend which addresses infinite-dimensional Lie groups. The results of this text are based on a theory of pro-Lie algebras which parallels the structure theory of finite-dimensional real Lie algebras to an astonishing degree, even though it has had to overcome greater technical obstacles. This book exposes a Lie theory of connected pro-Lie groups (and hence of connected locally compact groups) and illuminates the manifold ways in which their structure theory reduces to that of compact groups on the one hand and of finite-dimensional Lie groups on the other. It is a continuation of the authors' fundamental monograph on the structure of compact groups (1998, 2006) and is an invaluable tool for researchers in topological groups, Lie theory, harmonic analysis, and representation theory. It is written to be accessible to advanced graduate students wishing to study this fascinating and important area of current research, which has so many fruitful interactions with other fields of mathematics.

The Lie Theory Of Connected Pro Lie Groups

DOWNLOAD
Author : Karl Heinrich Hofmann
language : en
Publisher:
Release Date : 2007

The Lie Theory Of Connected Pro Lie Groups written by Karl Heinrich Hofmann and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Lie algebras categories.

Lie groups were introduced in 1870 by the Norwegian mathematician Sophus Lie. A century later Jean Dieudonné quipped that Lie groups had moved to the center of mathematics and that one cannot undertake anything without them. If a complete topological group $G$ can be approximated by Lie groups in the sense that every identity neighborhood $U$ of $G$ contains a normal subgroup $N$ such that $G/N$ is a Lie group, then it is called a pro-Lie group. Every locally compact connected topological group and every compact group is a pro-Lie group. While the class of locally compact groups is not closed under the formation of arbitrary products, the class of pro-Lie groups is. For half a century, locally compact pro-Lie groups have drifted through the literature, yet this is the first book which systematically treats the Lie and structure theory of pro-Lie groups irrespective of local compactness. This study fits very well into the current trend which addresses infinite-dimensional Lie groups. The results of this text are based on a theory of pro-Lie algebras which parallels the structure theory of finite-dimensional real Lie algebras to an astonishing degree, even though it has had to overcome greater technical obstacles. This book exposes a Lie theory of connected pro-Lie groups (and hence of connected locally compact groups) and illuminates the manifold ways in which their structure theory reduces to that of compact groups on the one hand and of finite-dimensional Lie groups on the other. It is a continuation of the authors' fundamental monograph on the structure of compact groups (1998, 2006) and is an invaluable tool for researchers in topological groups, Lie theory, harmonic analysis, and representation theory. It is written to be accessible to advanced graduate students wishing to study this fascinating and important area of current research, which has so many fruitful interactions with other fields of mathematics.

The Structure Of Pro Lie Groups

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Author : Karl H. Hofmann
language : en
Publisher:
Release Date : 2023

The Structure Of Pro Lie Groups written by Karl H. Hofmann and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023 with categories.

An Introduction To Infinite Dimensional Differential Geometry

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Author : Alexander Schmeding
language : en
Publisher: Cambridge University Press
Release Date : 2022-12-22

An Introduction To Infinite Dimensional Differential Geometry written by Alexander Schmeding and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-22 with Mathematics categories.

Introduces foundational concepts in infinite-dimensional differential geometry beyond Banach manifolds, showcasing its modern applications.

Journal Of Lie Theory

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Author :
language : en
Publisher:
Release Date : 2007

Journal Of Lie Theory written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Lie algebras categories.

The Structure Of Compact Groups

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Author : Karl H. Hofmann
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2023-10-24

The Structure Of Compact Groups written by Karl H. Hofmann and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-24 with Mathematics categories.

The subject matter of compact groups is frequently cited in fi elds like algebra, topology, functional analysis, and theoretical physics. This book serves the dual purpose of providing a text for upper level graduate students, and of being a source book for researchers who need the structure and representation theory of compact groups. After a gentle introduction to compact groups and their representation theory, the book presents self-contained courses on linear Lie groups and on locally compact abelian groups.Appended chapters contain the material for self-contained courses on abelian groups and on category theory.Using the Lie algebras and the exponential function of arbitrary compact groups, the book avoids unnecessary restrictions to finite dimensional or abelian compact groups. Earlier editions of 1998, 2006, 2013, and 2020 have been quoted for instruction and research. The present edition conceptually sharpens, polishes, and improves the earlier material. For instance, it includes a treatment of the Bohr compactifi cation of topological groups which fi ts perfectly into the general treatment of adjoint functors that the book treats in an appendix of its own, and which, in the abelian environment, connects neatly with the Pontryagin--van Kampen duality of compact abelian groups having been discussed in the book in great detail. The link between arbitrary compact groups and their weakly complete group algebras is as extensively discussed as is now the theory of weakly complete universal enveloping algebras of the Lie algebras of compact groups. All of this is based on the category of weakly complete real and complex vector spaces and its precise duality to the category of ordinary real, respectively, complex vector spaces, is treated in an appendix systematically.

Discrete Mechanics Geometric Integration And Lie Butcher Series

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Author : Kurusch Ebrahimi-Fard
language : en
Publisher: Springer
Release Date : 2018-11-05

Discrete Mechanics Geometric Integration And Lie Butcher Series written by Kurusch Ebrahimi-Fard and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-05 with Mathematics categories.

This volume resulted from presentations given at the international “Brainstorming Workshop on New Developments in Discrete Mechanics, Geometric Integration and Lie–Butcher Series”, that took place at the Instituto de Ciencias Matemáticas (ICMAT) in Madrid, Spain. It combines overview and research articles on recent and ongoing developments, as well as new research directions. Why geometric numerical integration? In their article of the same title Arieh Iserles and Reinout Quispel, two renowned experts in numerical analysis of differential equations, provide a compelling answer to this question. After this introductory chapter a collection of high-quality research articles aim at exploring recent and ongoing developments, as well as new research directions in the areas of geometric integration methods for differential equations, nonlinear systems interconnections, and discrete mechanics. One of the highlights is the unfolding of modern algebraic and combinatorial structures common to those topics, which give rise to fruitful interactions between theoretical as well as applied and computational perspectives. The volume is aimed at researchers and graduate students interested in theoretical and computational problems in geometric integration theory, nonlinear control theory, and discrete mechanics.

Topological Groups Yesterday Today Tomorrow

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Author : Sidney A. Morris
language : en
Publisher: MDPI
Release Date : 2018-09-27

Topological Groups Yesterday Today Tomorrow written by Sidney A. Morris and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-27 with Mathematics categories.

This book is a printed edition of the Special Issue "Topological Groups: Yesterday, Today, Tomorrow" that was published in Axioms

Modern Trends In Algebra And Representation Theory

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Author : David Jordan
language : en
Publisher: Cambridge University Press
Release Date : 2023-08-17

Modern Trends In Algebra And Representation Theory written by David Jordan and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-17 with Mathematics categories.

Aimed at graduate students and non-experts, this text gives a guided tour of modern developments in algebra and representation theory.

Topics In Noncommutative Algebra

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Author : Andrea Bonfiglioli
language : en
Publisher: Springer
Release Date : 2011-10-11

Topics In Noncommutative Algebra written by Andrea Bonfiglioli and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-11 with Mathematics categories.

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.