Exceptional Lie Algebras And The Structure Of Hermitian Symmetric Spaces
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Exceptional Lie Algebras And The Structure Of Hermitian Symmetric Spaces
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Author : Daniel Drucker
language : en
Publisher: American Mathematical Soc.
Release Date : 1978
Exceptional Lie Algebras And The Structure Of Hermitian Symmetric Spaces written by Daniel Drucker 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 1978 with Mathematics categories.
This monograph explicitly determines the "orbit structure" of all irreducible hermitian symmetric (IHS) spaces in a unified way by means of Lie algebra calculations, using J. Tits' models of the Lie algebras [script]e6 and [script]e7 in the two "exceptional" cases. An introduction to the theory of hermitian symmetric spaces is included, along with an elementary exposition of the facts from nonassociative algebra needed to understand and use Tits' constructions of all the complex exceptional simple Lie algebras and their real forms
Exceptional Lie Algebras And The Structure Of Hermitian Symmetric Spaces
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Author : American Mathematical Society
language : en
Publisher:
Release Date : 1978
Exceptional Lie Algebras And The Structure Of Hermitian Symmetric Spaces written by American Mathematical Society and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with Delay differential equations categories.
Differential Geometry Lie Groups And Symmetric Spaces
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Author : Sigurdur Helgason
language : en
Publisher: American Mathematical Society
Release Date : 2024-12-19
Differential Geometry Lie Groups And Symmetric Spaces written by Sigurdur Helgason and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-19 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. —André 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.
Locally Mixed Symmetric Spaces
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Author : Bruce Hunt
language : en
Publisher: Springer Nature
Release Date : 2021-09-04
Locally Mixed Symmetric Spaces written by Bruce Hunt and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-04 with Mathematics categories.
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.
Metric Rigidity Theorems On Hermitian Locally Symmetric Manifolds
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Author : Ngaiming Mok
language : en
Publisher: World Scientific
Release Date : 1989
Metric Rigidity Theorems On Hermitian Locally Symmetric Manifolds written by Ngaiming Mok and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Mathematics categories.
This monograph studies the problem of characterizing canonical metrics on Hermitian locally symmetric manifolds X of non-compact/compact types in terms of curvature conditions. The proofs of these metric rigidity theorems are applied to the study of holomorphic mappings between manifolds X of the same type. Moreover, a dual version of the generalized Frankel Conjecture on characterizing compact Khler manifolds are also formulated.
Algebraic Structures Of Symmetric Domains
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Author : Ichiro Satake
language : en
Publisher: Princeton University Press
Release Date : 2014-07-14
Algebraic Structures Of Symmetric Domains written by Ichiro Satake and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-14 with Mathematics categories.
This book is a comprehensive treatment of the general (algebraic) theory of symmetric domains. Originally published in 1981. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Harmonic Analysis On Commutative Spaces
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Author : Joseph Albert Wolf
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
Harmonic Analysis On Commutative Spaces written by Joseph Albert Wolf 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 2007 with Mathematics categories.
This study starts with the basic theory of topological groups, harmonic analysis, and unitary representations. It then concentrates on geometric structure, harmonic analysis, and unitary representation theory in commutative spaces.
Exceptional Lie Groups
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Author : Ichiro Yokota
language : en
Publisher: Springer Nature
Release Date : 2025-06-30
Exceptional Lie Groups written by Ichiro Yokota and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-30 with Mathematics categories.
This book provides a concrete description of the identity connected components of the real and complex exceptional Lie groups. The constructions are elementary and improve on those of H. Freudenthal. The complex simple Lie algebras were classified into classical (An, Bn, Cn, Dn) and exceptional (G2, F4, E6, E7, E8) types at the end of the 19th century by W. Killing and É. Cartan. These simple Lie algebras and the corresponding compact simple Lie groups arise in many settings in mathematics and physics. The exceptional Lie groups form an especially interesting class of objects that have attracted the attention of numerous mathematicians. Requiring no prior knowledge of composition algebras or Jordan algebras, the book will be valuable to anyone who wants to learn about the structure and realizations of these fascinating groups.
Complex Analysis And Potential Theory
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Author : Andre Boivin
language : en
Publisher: American Mathematical Soc.
Release Date : 2012
Complex Analysis And Potential Theory written by Andre Boivin 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 2012 with Mathematics categories.
This is the proceedings volume of an international conference entitled Complex Analysis and Potential Theory, which was held to honor the important contributions of two influential analysts, Kohur N. GowriSankaran and Paul M. Gauthier, in June 2011 at the Centre de Recherches Mathematiques (CRM) in Montreal. More than fifty mathematicians from fifteen countries participated in the conference. The twenty-four surveys and research articles contained in this book are based on the lectures given by some of the most established specialists in the fields. They reflect the wide breadth of research interests of the two honorees: from potential theory on trees to approximation on Riemann surfaces, from universality to inner and outer functions and the disc algebra, from branching processes to harmonic extension and capacities, from harmonic mappings and the Harnack principle to integration formulae in $\mathbb {C}^n$ and the Hartogs phenomenon, from fine harmonicity and plurisubharmonic functions to the binomial identity and the Riemann hypothesis, and more. This volume will be a valuable resource for specialists, young researchers, and graduate students from both fields, complex analysis and potential theory. It will foster further cooperation and the exchange of ideas and techniques to find new research perspectives.
The Schwarz Lemma
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Author : Sean Dineen
language : en
Publisher: Courier Dover Publications
Release Date : 2016-04-06
The Schwarz Lemma written by Sean Dineen and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-06 with Mathematics categories.
Suitable for advanced undergraduates and graduate students, this self-contained overview covers the classical Schwarz lemma, Poincaré distance on the unit disc, hyperbolic manifolds, holomorphic curvature, and the analytic Radon-Nikodym property. 1989 edition.