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The Structural Lie tackles one of social science's most mysterious problems. How is it possible to derive statements about the grand structures of social life from their effects in the small movements of everyday life? Prominent sociologist Charles Lemert shows how Marx and Freud provide some answers to this question. Marx derived from the commodity his picture of the capitalist system, Freud diagnosed the character of psyches from the details of dreams, slips and jokes. This wonderfully readable and engaging book lays the foundation for a new social science in an age where a microchip can convey a world of information.
Lie's Structural Approach to PDE Systems by Olle Stormark Pdf
Here is a lucid and comprehensive introduction to the differential geometric study of partial differential equations (PDE). The first book to present substantial results on local solvability of general and nonlinear PDE systems without using power series techniques, it describes a general approach to PDE systems based on ideas developed by Lie, Cartan and Vessiot. The central theme is the exploitation of singular vector field systems and their first integrals. These considerations naturally lead to local Lie groups, Lie pseudogroups and the equivalence problem, all of which are covered in detail. This book will be a valuable resource for graduate students and researchers in partial differential equations, Lie groups and related fields.
A Guide To Lie Systems With Compatible Geometric Structures by Javier De Lucas Araujo,Cristina Sardon Munoz Pdf
The book presents a comprehensive guide to the study of Lie systems from the fundamentals of differential geometry to the development of contemporary research topics. It embraces several basic topics on differential geometry and the study of geometric structures while developing known applications in the theory of Lie systems. The book also includes a brief exploration of the applications of Lie systems to superequations, discrete systems, and partial differential equations.Offering a complete overview from the topic's foundations to the present, this book is an ideal resource for Physics and Mathematics students, doctoral students and researchers.
Jordan Structures in Lie Algebras by Antonio Fernández López Pdf
Explores applications of Jordan theory to the theory of Lie algebras. After presenting the general theory of nonassociative algebras and of Lie algebras, the book then explains how properties of the Jordan algebra attached to a Jordan element of a Lie algebra can be used to reveal properties of the Lie algebra itself.
The Geometry of Jordan and Lie Structures by Wolfgang Bertram Pdf
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.
Structure and Geometry of Lie Groups by Joachim Hilgert,Karl-Hermann Neeb Pdf
This self-contained text is an excellent introduction to Lie groups and their actions on manifolds. The authors start with an elementary discussion of matrix groups, followed by chapters devoted to the basic structure and representation theory of finite dimensinal Lie algebras. They then turn to global issues, demonstrating the key issue of the interplay between differential geometry and Lie theory. Special emphasis is placed on homogeneous spaces and invariant geometric structures. The last section of the book is dedicated to the structure theory of Lie groups. Particularly, they focus on maximal compact subgroups, dense subgroups, complex structures, and linearity. This text is accessible to a broad range of mathematicians and graduate students; it will be useful both as a graduate textbook and as a research reference.
The Structural Lie tackles one of social science's most mysterious problems. How is it possible to derive statements about the grand structures of social life from their effects in the small movements of everyday life? Prominent sociologist Charles Lemert shows how Marx and Freud provide some answers to this question. Marx derived from the commodity his picture of the capitalist system, Freud diagnosed the character of psyches from the details of dreams, slips and jokes. This wonderfully readable and engaging book lays the foundation for a new social science in an age where a microchip can convey a world of information.
The Structure of Complex Lie Groups by Dong Hoon Lee Pdf
Complex Lie groups have often been used as auxiliaries in the study of real Lie groups in areas such as differential geometry and representation theory. To date, however, no book has fully explored and developed their structural aspects. The Structure of Complex Lie Groups addresses this need. Self-contained, it begins with general concepts introduced via an almost complex structure on a real Lie group. It then moves to the theory of representative functions of Lie groups- used as a primary tool in subsequent chapters-and discusses the extension problem of representations that is essential for studying the structure of complex Lie groups. This is followed by a discourse on complex analytic groups that carry the structure of affine algebraic groups compatible with their analytic group structure. The author then uses the results of his earlier discussions to determine the observability of subgroups of complex Lie groups. The differences between complex algebraic groups and complex Lie groups are sometimes subtle and it can be difficult to know which aspects of algebraic group theory apply and which must be modified. The Structure of Complex Lie Groups helps clarify those distinctions. Clearly written and well organized, this unique work presents material not found in other books on Lie groups and serves as an outstanding complement to them.
Lie Algebras and Related Topics by Daniel J. Britten,Frank W. Lemire,R. V. Moody Pdf
As the Proceedings of the 1984 Canadian Mathematical Society's Summer Seminar, this book focuses on some advances in the theory of semisimple Lie algebras and some direct outgrowths of that theory. The following papers are of particular interest: an important survey article by R. Block and R. Wilson on restricted simple Lie algebras, a survey of universal enveloping algebras of semisimple Lie algebras by W. Borho, a course on Kac-Moody Lie algebras by I. G. Macdonald with an extensive bibliography of this field by Georgia Benkart, and a course on formal groups by M. Hazewinkel. Because of the expository surveys and courses, the book will be especially useful to graduate students in Lie theory, as well as to researchers in the field.
Lectures On Lie Groups (Second Edition) by Hsiang Wu-yi Pdf
This volume consists of nine lectures on selected topics of Lie group theory. We provide the readers a concise introduction as well as a comprehensive "tour of revisiting" the remarkable achievements of S Lie, W Killing, É Cartan and H Weyl on structural and classification theory of semi-simple Lie groups, Lie algebras and their representations; and also the wonderful duet of Cartan's theory on Lie groups and symmetric spaces. With the benefit of retrospective hindsight, mainly inspired by the outstanding contribution of H Weyl in the special case of compact connected Lie groups, we develop the above theory via a route quite different from the original methods engaged by most other books. We begin our revisiting with the compact theory which is much simpler than that of the general semi-simple Lie theory; mainly due to the well fittings between the Frobenius–Schur character theory and the maximal tori theorem of É Cartan together with Weyl's reduction (cf. Lectures 1–4). It is a wonderful reality of the Lie theory that the clear-cut orbital geometry of the adjoint action of compact Lie groups on themselves (i.e. the geometry of conjugacy classes) is not only the key to understand the compact theory, but it actually already constitutes the central core of the entire semi-simple theory, as well as that of the symmetric spaces (cf. Lectures 5– 9). This is the main reason that makes the succeeding generalizations to the semi-simple Lie theory, and then further to the Cartan theory on Lie groups and symmetric spaces, conceptually quite natural, and technically rather straightforward.
Symplectic Manifolds with no Kaehler structure by Alesky Tralle,John Oprea Pdf
This is a research monograph covering the majority of known results on the problem of constructing compact symplectic manifolds with no Kaehler structure with an emphasis on the use of rational homotopy theory. In recent years, some new and stimulating conjectures and problems have been formulated due to an influx of homotopical ideas. Examples include the Lupton-Oprea conjecture, the Benson-Gordon conjecture, both of which are in the spirit of some older and still unsolved problems (e.g. Thurston's conjecture and Sullivan's problem). Our explicit aim is to clarify the interrelations between certain aspects of symplectic geometry and homotopy theory in the framework of the problems mentioned above. We expect that the reader is aware of the basics of differential geometry and algebraic topology at graduate level.
Handbook of Seismic Risk Analysis and Management of Civil Infrastructure Systems by S Tesfamariam,K Goda Pdf
Earthquakes represent a major risk to buildings, bridges and other civil infrastructure systems, causing catastrophic loss to modern society. Handbook of seismic risk analysis and management of civil infrastructure systems reviews the state of the art in the seismic risk analysis and management of civil infrastructure systems. Part one reviews research in the quantification of uncertainties in ground motion and seismic hazard assessment. Part twi discusses methodologies in seismic risk analysis and management, whilst parts three and four cover the application of seismic risk assessment to buildings, bridges, pipelines and other civil infrastructure systems. Part five also discusses methods for quantifying dependency between different infrastructure systems. The final part of the book considers ways of assessing financial and other losses from earthquake damage as well as setting insurance rates. Handbook of seismic risk analysis and management of civil infrastructure systems is an invaluable guide for professionals requiring understanding of the impact of earthquakes on buildings and lifelines, and the seismic risk assessment and management of buildings, bridges and transportation. It also provides a comprehensive overview of seismic risk analysis for researchers and engineers within these fields. This important handbook reviews the wealth of recent research in the area of seismic hazard analysis in modern earthquake design code provisions and practices Examines research into the analysis of ground motion and seismic hazard assessment, seismic risk hazard methodologies Addresses the assessment of seismic risks to buildings, bridges, water supply systems and other aspects of civil infrastructure
Tubular Structures XV by Eduardo de Miranda Batista,Pedro Vellasco,Luciano Rodrigues Ornelas de Lima Pdf
Tubular Structures XV contains the latest scientific and engineering developments in the field of tubular structures, as presented at the 15th International Symposium on Tubular Structures (ISTS15, Rio de Janeiro, Brazil, 27-29 May 2015). The International Symposium on Tubular Structures (ISTS) has a long-standing reputation for being the principal
Crystal Structure Analysis by Jenny Pickworth Glusker,Kenneth N. Trueblood Pdf
The purpose of this book is to explain why molecular structure can be determined by single-crystal diffraction of X rays. It is not an account of the practical procedural details, but rather an account of the underlying physical principles, and the kinds of experiments and methods of handling the experimental data that are used.