Differential Geometry, Lie Groups, and Symmetric Spaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Differential Geometry, Lie Groups, and Symmetric Spaces write by Sigurdur Helgason. This book was released on 2001-06-12. Differential Geometry, Lie Groups, and Symmetric Spaces available in PDF, EPUB and Kindle. 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.
Semisimple Groups and Riemannian Symmetric Spaces
Semisimple Groups and Riemannian Symmetric Spaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Semisimple Groups and Riemannian Symmetric Spaces write by Armand Borel. This book was released on 1998-12-15. Semisimple Groups and Riemannian Symmetric Spaces available in PDF, EPUB and Kindle.
Lie Groups and Symmetric Spaces
Lie Groups and Symmetric Spaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lie Groups and Symmetric Spaces write by Semen Grigorʹevich Gindikin. This book was released on 2003. Lie Groups and Symmetric Spaces available in PDF, EPUB and Kindle. The book contains survey and research articles devoted mainly to geometry and harmonic analysis of symmetric spaces and to corresponding aspects of group representation theory. The volume is dedicated to the memory of Russian mathematician, F. I. Karpelevich (1927-2000). Of particular interest are the survey articles by Sawyer on the Abel transform on noncompact Riemannian symmetric spaces, and by Anker and Ostellari on estimates for heat kernels on such spaces, as well as thearticle by Bernstein and Gindikin on integral geometry for families of curves. There are also many research papers on topics of current interest. The book is suitable for graduate students and research mathematicians interested in harmonic analysis and representation theory.
Integrable Systems on Lie Algebras and Symmetric Spaces
Integrable Systems on Lie Algebras and Symmetric Spaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Integrable Systems on Lie Algebras and Symmetric Spaces write by A. T. Fomenko. This book was released on 1988. Integrable Systems on Lie Algebras and Symmetric Spaces available in PDF, EPUB and Kindle. Second volume in the series, translated from the Russian, sets out new regular methods for realizing Hamilton's canonical equations in Lie algebras and symmetric spaces. Begins by constructing the algebraic embeddings in Lie algebras of Hamiltonian systems, going on to present effective methods for constructing complete sets of functions in involution on orbits of coadjoint representations of Lie groups. Ends with the proof of the full integrability of a wide range of many- parameter families of Hamiltonian systems that allow algebraicization. Annotation copyrighted by Book News, Inc., Portland, OR
Locally Mixed Symmetric Spaces
Locally Mixed Symmetric Spaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Locally Mixed Symmetric Spaces write by Bruce Hunt. This book was released on 2021-09-04. Locally Mixed Symmetric Spaces available in PDF, EPUB and Kindle. What do the classification of algebraic surfaces, Weyl's dimension formula and maximal orders in central simple algebras have in common? All are related to a type of manifold called locally mixed symmetric spaces in this book. The presentation emphasizes geometric concepts and relations and gives each reader the "roter Faden", starting from the basics and proceeding towards quite advanced topics which lie at the intersection of differential and algebraic geometry, algebra and topology. Avoiding technicalities and assuming only a working knowledge of real Lie groups, the text provides a wealth of examples of symmetric spaces. The last two chapters deal with one particular case (Kuga fiber spaces) and a generalization (elliptic surfaces), both of which require some knowledge of algebraic geometry. Of interest to topologists, differential or algebraic geometers working in areas related to arithmetic groups, the book also offers an introduction to the ideas for non-experts.
