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Author: Daniel Drucker Publisher: American Mathematical Soc. ISBN: 082182208X Category : Exceptional Lie algebras Languages : en Pages : 215
Book Description
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
Author: Daniel Drucker Publisher: American Mathematical Soc. ISBN: 082182208X Category : Exceptional Lie algebras Languages : en Pages : 215
Book Description
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
Author: A. T. Fomenko Publisher: CRC Press ISBN: 9782881241703 Category : Mathematics Languages : en Pages : 316
Book Description
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
Author: Ichiro Satake Publisher: Princeton University Press ISBN: 1400856809 Category : Mathematics Languages : en Pages : 340
Book Description
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.
Author: Bruce Hunt Publisher: Springer Nature ISBN: 3030698041 Category : Mathematics Languages : en Pages : 622
Book Description
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.
Author: Jacques Faraut Publisher: Springer Science & Business Media ISBN: 9780817641382 Category : Mathematics Languages : en Pages : 568
Book Description
A number of important topics in complex analysis and geometry are covered in this excellent introductory text. Written by experts in the subject, each chapter unfolds from the basics to the more complex. The exposition is rapid-paced and efficient, without compromising proofs and examples that enable the reader to grasp the essentials. The most basic type of domain examined is the bounded symmetric domain, originally described and classified by Cartan and Harish- Chandra. Two of the five parts of the text deal with these domains: one introduces the subject through the theory of semisimple Lie algebras (Koranyi), and the other through Jordan algebras and triple systems (Roos). Larger classes of domains and spaces are furnished by the pseudo-Hermitian symmetric spaces and related R-spaces. These classes are covered via a study of their geometry and a presentation and classification of their Lie algebraic theory (Kaneyuki). In the fourth part of the book, the heat kernels of the symmetric spaces belonging to the classical Lie groups are determined (Lu). Explicit computations are made for each case, giving precise results and complementing the more abstract and general methods presented. Also explored are recent developments in the field, in particular, the study of complex semigroups which generalize complex tube domains and function spaces on them (Faraut). This volume will be useful as a graduate text for students of Lie group theory with connections to complex analysis, or as a self-study resource for newcomers to the field. Readers will reach the frontiers of the subject in a considerably shorter time than with existing texts.
Author: Sigurdur Helgason Publisher: American Mathematical Soc. ISBN: 0821828487 Category : Mathematics Languages : en Pages : 682
Book Description
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.
Author: Ngaiming Mok Publisher: World Scientific ISBN: 9789971508005 Category : Mathematics Languages : en Pages : 296
Book Description
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 KÂhler manifolds are also formulated.
Author: Wolfgang Bertram Publisher: Springer Science & Business Media ISBN: 3540414266 Category : Mathematics Languages : en Pages : 285
Book Description
The geometry of Jordan and Lie structures tries to answer the following question: what is the integrated, or geometric, version of real Jordan algebras, - triple systems and - pairs? Lie theory shows the way one has to go: Lie groups and symmetric spaces are the geometric version of Lie algebras and Lie triple systems. It turns out that both geometries are closely related via a functor between them, called the Jordan-Lie functor, which is constructed in this book. The reader is not assumed to have any knowledge of Jordan theory; the text can serve as a self-contained introduction to (real finite-dimensional) Jordan theory.
Author: Daniel Drucker
Author: Daniel Drucker
Author: American Mathematical Society
Author: A. T. Fomenko
Author: Ichiro Satake
Author: Bruce Hunt
Author: Jacques Faraut
Author: Khalid Koufany
Author: Sigurdur Helgason
Author: Ngaiming Mok
Author: Wolfgang Bertram