گروه‌های لی

The first part of this book, which is the second edition of the book of the same title, is intended to provide readers with a brief introduction to the theory of Lie groups as an aid to further study by presenting the fundamental features of Lie groups as a starting point for understanding Lie algebras and Lie theory in general. In the revisions for the second edition, proofs of some of the results were added. The second part of the book builds on some of the background developed in the first part, offering an introduction to the theory of symmetric spaces, a remarkable example of applications of Lie group theory to differential geometry. The book emphasizes this aspect by surveying the fundamentals of Riemannian manifolds and by giving detailed explanations of the way in which geometry and Lie group theory come together. Cover Title page Contents Lie Groups I Contents of Lie Groups I Preface to Lie Groups I Foreword to Lie Groups I Foreword to the First Edition of Lie Groups I Notation to Lie Groups I Chapter I. Concept of Lie group, particularly, linear Lie group Chapter II. Compact Lie groups and semisimple Lie groups Chapter III. Outline of the theory of Lie algebras References Lie Groups II Contents of Lie Groups II Preface to Lie Groups II Foreword to Lie Groups II Chapter I. Riemannian manifolds Chapter II. Riemannian symmetric spaces Chapter III. Riemannian symmetric spaces of semisimple type Chapter I. Hermitian symmetric spaces References Back Cover Presents a wide range of problems connected with rational approximations of numbers and analytic functions; these problems touch on many topics in contemporary analysis, such as analytic functions, orthogonal polynomials, spectral theory of operators, and potential theory. Mikio Ise, Masaru Takeuchi. Lie Groups Ii / Masaru Takeuchi. Translation Of: Rī-gun. Includes Bibliographical References.