An Introduction To Lie Groups And The Geometry Of Homogeneous Spaces
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An Introduction To Lie Groups And The Geometry Of Homogeneous Spaces
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Author : Andreas Arvanitogeōrgos
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
An Introduction To Lie Groups And The Geometry Of Homogeneous Spaces written by Andreas Arvanitogeōrgos and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Homogeneous spaces categories.
It is remarkable that so much about Lie groups could be packed into this small book. But after reading it, students will be well-prepared to continue with more advanced, graduate-level topics in differential geometry or the theory of Lie groups. The theory of Lie groups involves many areas of mathematics. In this book, Arvanitoyeorgos outlines enough of the prerequisites to get the reader started. He then chooses a path through this rich and diverse theory that aims for an understanding of the geometry of Lie groups and homogeneous spaces. In this way, he avoids the extra detail needed for a thorough discussion of other topics. Lie groups and homogeneous spaces are especially useful to study in geometry, as they provide excellent examples where quantities (such as curvature) are easier to compute. A good understanding of them provides lasting intuition, especially in differential geometry. The book is suitable for advanced undergraduates, graduate students, and research mathematicians interested in differential geometry and neighboring fields, such as topology, harmonic analysis, and mathematical physics.
Differential Geometry Lie Groups And Symmetric Spaces
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Author : Sigurdur Helgason
language : en
Publisher: American Mathematical Soc.
Release Date : 2001-06-12
Differential Geometry Lie Groups And Symmetric Spaces written by Sigurdur Helgason and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-06-12 with Mathematics categories.
A great book ... a necessary item in any mathematical library. --S. S. Chern, University of California A brilliant book: rigorous, tightly organized, and covering a vast amount of good mathematics. --Barrett O'Neill, University of California This is obviously a very valuable and well thought-out book on an important subject. --Andre Weil, Institute for Advanced Study The study of homogeneous spaces provides excellent insights into both differential geometry and Lie groups. In geometry, for instance, general theorems and properties will also hold for homogeneous spaces, and will usually be easier to understand and to prove in this setting. For Lie groups, a significant amount of analysis either begins with or reduces to analysis on homogeneous spaces, frequently on symmetric spaces. For many years and for many mathematicians, Sigurdur Helgason's classic Differential Geometry, Lie Groups, and Symmetric Spaces has been--and continues to be--the standard source for this material. Helgason begins with a concise, self-contained introduction to differential geometry. Next is a careful treatment of the foundations of the theory of Lie groups, presented in a manner that since 1962 has served as a model to a number of subsequent authors. This sets the stage for the introduction and study of symmetric spaces, which form the central part of the book. The text concludes with the classification of symmetric spaces by means of the Killing-Cartan classification of simple Lie algebras over $\mathbb{C}$ and Cartan's classification of simple Lie algebras over $\mathbb{R}$, following a method of Victor Kac. The excellent exposition is supplemented by extensive collections of useful exercises at the end of each chapter. All of the problems have either solutions or substantial hints, found at the back of the book. For this edition, the author has made corrections and added helpful notes and useful references. Sigurdur Helgason was awarded the Steele Prize for Differential Geometry, Lie Groups, and Symmetric Spaces and Groups and Geometric Analysis.
An Introduction To Lie Groups And Lie Algebras
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Author : Alexander Kirillov, Jr
language : en
Publisher: Cambridge University Press
Release Date : 2017-06-30
An Introduction To Lie Groups And Lie Algebras written by Alexander Kirillov, Jr 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 2017-06-30 with Mathematics categories.
This classic graduate text focuses on the study of semisimple Lie algebras, developing the necessary theory along the way. The material covered ranges from basic definitions of Lie groups to the classification of finite-dimensional representations of semisimple Lie algebras. Lie theory, in its own right, has become regarded as a classical branch of mathematics. Written in an informal style, this is a contemporary introduction to the subject which emphasizes the main concepts of the proofs and outlines the necessary technical details, allowing the material to be conveyed concisely. Based on a lecture course given by the author at the State University of New York at Stony Brook, the book includes numerous exercises and worked examples and is ideal for graduate courses on Lie groups and Lie algebras.
An Introduction To Lie Groups And The Geometry Of Homogeneous Spaces
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Author : Andreas Arvanitogeōrgos
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
An Introduction To Lie Groups And The Geometry Of Homogeneous Spaces written by Andreas Arvanitogeōrgos and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
This author packs a lot of punch in this small book. It presents enough background detail to allow those looking for an introduction to the topic to begin learning without mastering a lot of prerequisites. He provides several good examples and computations, making it an excellent text for advanced undergraduate and graduate courses. The topics covered in this book provide the student with a sound base for understanding how things work in other areas, especially in differential geometry.
Lie Groups
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Author : Luiz A. B. San Martin
language : en
Publisher: Springer Nature
Release Date : 2021-02-23
Lie Groups written by Luiz A. B. San Martin and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-23 with Mathematics categories.
This textbook provides an essential introduction to Lie groups, presenting the theory from its fundamental principles. Lie groups are a special class of groups that are studied using differential and integral calculus methods. As a mathematical structure, a Lie group combines the algebraic group structure and the differentiable variety structure. Studies of such groups began around 1870 as groups of symmetries of differential equations and the various geometries that had emerged. Since that time, there have been major advances in Lie theory, with ramifications for diverse areas of mathematics and its applications. Each chapter of the book begins with a general, straightforward introduction to the concepts covered; then the formal definitions are presented; and end-of-chapter exercises help to check and reinforce comprehension. Graduate and advanced undergraduate students alike will find in this book a solid yet approachable guide that will help them continue their studies with confidence.
Matrix Groups
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Author : Andrew Baker
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Matrix Groups written by Andrew Baker and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Aimed at advanced undergraduate and beginning graduate students, this book provides a first taste of the theory of Lie groups as an appetiser for a more substantial further course. Lie theoretic ideas lie at the heart of much of standard undergraduate linear algebra and exposure to them can inform or motivate the study of the latter. The main focus is on matrix groups, i.e., closed subgroups of real and complex general linear groups. The first part studies examples and describes the classical families of simply connected compact groups. The second part introduces the idea of a lie group and studies the associated notion of a homogeneous space using orbits of smooth actions. Throughout, the emphasis is on providing an approach that is accessible to readers equipped with a standard undergraduate toolkit of algebra and analysis. Although the formal prerequisites are kept as low level as possible, the subject matter is sophisticated and contains many of the key themes of the fully developed theory, preparing students for a more standard and abstract course in Lie theory and differential geometry.
Foundations Of Differentiable Manifolds And Lie Groups
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Author : Frank W. Warner
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Foundations Of Differentiable Manifolds And Lie Groups written by Frank W. Warner and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Mathematics categories.
Foundations of Differentiable Manifolds and Lie Groups gives a clear, detailed, and careful development of the basic facts on manifold theory and Lie Groups. It includes differentiable manifolds, tensors and differentiable forms. Lie groups and homogenous spaces, integration on manifolds, and in addition provides a proof of the de Rham theorem via sheaf cohomology theory, and develops the local theory of elliptic operators culminating in a proof of the Hodge theorem. Those interested in any of the diverse areas of mathematics requiring the notion of a differentiable manifold will find this beginning graduate-level text extremely useful.
Lie Groups
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Author : Wulf Rossmann
language : en
Publisher: OUP Oxford
Release Date : 2006
Lie Groups written by Wulf Rossmann and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Business & Economics categories.
Lie Groups is intended as an introduction to the theory of Lie groups and their representations at the advanced undergraduate or beginning graduate level. It covers the essentials of the subject starting from basic undergraduate mathematics. The correspondence between linear Lie groups and Lie algebras is developed in its local and global aspects. The classical groups are analysed in detail, first with elementary matrix methods, then with the help of the structural tools typical of the theory of semisimple groups, such as Cartan subgroups, roots, weights, and reflections. The fundamental groups of the classical groups are worked out as an application of these methods. Manifolds are introduced when needed, in connection with homogeneous spaces, and the elements of differential and integral calculus on manifolds are presented, with special emphasis on integration on groups and homogeneous spaces. Representation theory starts from first principles, such as Schur's lemma and its consequences, and proceeds from there to the Peter-Weyl theorem, Weyl's character formula, and the Borel-Weil theorem, all in the context of linear groups.
Lectures On Lie Groups
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Author : J. F. Adams
language : en
Publisher: University of Chicago Press
Release Date : 1982
Lectures On Lie Groups written by J. F. Adams and has been published by University of Chicago Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with Mathematics categories.
"[Lectures in Lie Groups] fulfills its aim admirably and should be a useful reference for any mathematician who would like to learn the basic results for compact Lie groups. . . . The book is a well written basic text [and Adams] has done a service to the mathematical community."—Irving Kaplansky
Differential Geometry And Lie Groups
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Author : Jean Gallier
language : en
Publisher: Springer Nature
Release Date : 2020-08-18
Differential Geometry And Lie Groups written by Jean Gallier and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-18 with Mathematics categories.
This textbook explores advanced topics in differential geometry, chosen for their particular relevance to modern geometry processing. Analytic and algebraic perspectives augment core topics, with the authors taking care to motivate each new concept. Whether working toward theoretical or applied questions, readers will appreciate this accessible exploration of the mathematical concepts behind many modern applications. Beginning with an in-depth study of tensors and differential forms, the authors go on to explore a selection of topics that showcase these tools. An analytic theme unites the early chapters, which cover distributions, integration on manifolds and Lie groups, spherical harmonics, and operators on Riemannian manifolds. An exploration of bundles follows, from definitions to connections and curvature in vector bundles, culminating in a glimpse of Pontrjagin and Chern classes. The final chapter on Clifford algebras and Clifford groups draws the book to an algebraic conclusion, which can be seen as a generalized viewpoint of the quaternions. Differential Geometry and Lie Groups: A Second Course captures the mathematical theory needed for advanced study in differential geometry with a view to furthering geometry processing capabilities. Suited to classroom use or independent study, the text will appeal to students and professionals alike. A first course in differential geometry is assumed; the authors’ companion volume Differential Geometry and Lie Groups: A Computational Perspective provides the ideal preparation.