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This book explores how different social psychology theories and concepts can be applied to practice. Considering theories from attribution theory to coercion theory, social identity theories to ostracism, the authors offer a greater understanding and appreciation of the ways in which social psychology can contribute to forensic practice.

The subjects described in the book are BCC-algebras and an even wider class of weak BCC-algebras. The aim of the book is to summarize the achievements to date in the subject and to present them in the form of a logically created theory.

Social Communication Development and Disorders examines the integrated development of social, linguistic, and cognitive functions. It provides evidence-based clinical information on effective assessment and intervention for individuals with social communication disorders.

Presenting classical mechanics, quantum mechanics, and statistical mechanics in an almost completely algebraic setting, this monograph introduces mathematicians, physicists, and engineers to the ideas relating classical and quantum mechanics with Lie algebras and Lie groups. The focus lies on discussing structural properties of mechanics rather than computational techniques.

Eugene Wigner is one of the few giants of 20th-century physics. His early work helped to shape quantum mechanics, he laid the foundations of nuclear physics and nuclear engineering, and he contributed significantly to solid-state physics. His philosophical and political writings are widely known. All his works will be reprinted in Eugene Paul Wigner's Collected Workstogether with descriptive annotations by outstanding scientists. The present volume begins with a short biographical sketch followed by Wigner's papers on group theory, an extremely powerful tool he created for theoretical quantum physics. They are presented in two parts. The first, annotated by B. Judd, covers applications to atomic and molecular spectra, term structure, time reversal and spin. In the second, G. Mackey introduces to the reader the mathematical papers, many of which are outstanding contributions to the theory of unitary representations of groups, including the famous paper on the Lorentz group.

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.

With wide-ranging connections to fields from theoretical physics to computer science, Hopf algebras offer students a glimpse at the applications of abstract mathematics. This book is unique in making this engaging subject accessible to advanced undergraduate and beginning graduate students. After providing a self-contained introduction to group and ring theory, the book thoroughly treats the concept of the spectrum of a ring and the Zariski topology. In this way the student transitions smoothly from basic abstract algebra to Hopf algebras. The importance of Hopf orders is underscored with applications to algebraic number theory, Galois module theory and the theory of formal groups. By the end of the book, readers will be familiar with established results in the field and ready to pose research questions of their own.

In the 1970's, James developped a ``characterictic-free'' approach to the representation theory of the symmetric group on n letters, where Specht modules and certain bilinear forms on them play a crucial role. In this framework, we obtain a natural parametrization of the irreducible representations, but it is a major open problem to find explicit formulae for their dimensions when the ground field has positive characteristic.In a wider context, this problem is a special case of the problem of determining the irreducible representations of Iwahori--Hecke algebras at roots of unity. These algebras arise naturally in the representation theory of finite groups of Lie type, but they can be defined abstractly, as certain deformations of group algebras of finite Coxeter groups where the deformation depends on one or several parameters. One of the main aims of this book is to classify the irreducible representations of these Iwahori-Hecke algebras algebras at roots of unity. For this purpose, we develop an analogue of James' ``characterictic-free'' approach to the representation theory of Iwahori-Hecke algebras in general. The framework is provided by the Kazhdan-Lusztig theory of cells and the Graham-Lehrer theory of cellular algebras. When working over a ground field of characteristic zero, we also determine the dimensions of the irreducible representations, either by purely combinatorial algorithms (for algebras of classical type) or by explicit computations and tables (for algebras of exceptional type). The methods rely in an essential way on the ideas and results originating with the Lascoux-Leclerc-Thibon conjecture, which links Iwahori-Hecke algebras at roots of unity with the theory of canonical and crystal bases for the Fock space representations of certain affine Lie algebras. Thus, the main results of this book are obtained by an interaction of several branches of mathematics: Fock spaces and affine Lie algebras, the combinatorics of crystal bases, the theory of Kazhdan-Lusztig bases and cells, and computational methods.

(Cartan sub Lie algebra, roots, Weyl group, Dynkin diagram, . . . ) and the classification, as found by Killing and Cartan (the list of all semisimple Lie algebras consists of (1) the special- linear ones, i. e. all matrices (of any fixed dimension) with trace 0, (2) the orthogonal ones, i. e. all skewsymmetric ma- trices (of any fixed dimension), (3) the symplectic ones, i. e. all matrices M (of any fixed even dimension) that satisfy M J = - J MT with a certain non-degenerate skewsymmetric matrix J, and (4) five special Lie algebras G2, F , E , E , E , of dimensions 14,52,78,133,248, the "e;exceptional Lie 4 6 7 s algebras"e; , that just somehow appear in the process). There is also a discus- sion of the compact form and other real forms of a (complex) semisimple Lie algebra, and a section on automorphisms. The third chapter brings the theory of the finite dimensional representations of a semisimple Lie alge- bra, with the highest or extreme weight as central notion. The proof for the existence of representations is an ad hoc version of the present standard proof, but avoids explicit use of the Poincare-Birkhoff-Witt theorem. Complete reducibility is proved, as usual, with J. H. C. Whitehead's proof (the first proof, by H. Weyl, was analytical-topological and used the exis- tence of a compact form of the group in question). Then come H.

Recent major advances in model theory include connections between model theory and Diophantine and real analytic geometry, permutation groups, and finite algebras. The present book contains lectures on recent results in algebraic model theory, covering topics from the following areas: geometric model theory, the model theory of analytic structures, permutation groups in model theory, the spectra of countable theories, and the structure of finite algebras. Audience: Graduate students in logic and others wishing to keep abreast of current trends in model theory. The lectures contain sufficient introductory material to be able to grasp the recent results presented.

Foundations of Differentiable Manifolds and Lie Groups gives a clear, detailed, and careful development of the basic facts on manifold theory and Lie Groups. It includes differentiable manifolds, tensors and differentiable forms. Lie groups and homogenous spaces, integration on manifolds, and in addition provides a proof of the de Rham theorem via sheaf cohomology theory, and develops the local theory of elliptic operators culminating in a proof of the Hodge theorem. Those interested in any of the diverse areas of mathematics requiring the notion of a differentiable manifold will find this beginning graduate-level text extremely useful.

From reviews of the German edition: "This is an exciting text and a refreshing contribution to an area in which challenges continue to flourish and to captivate the viewer. Even though representation theory and constructions of simple groups have been omitted, the text serves as a springboard for deeper study in many directions. One who completes this text not only gains an appreciation of both the depth and the breadth of the theory of finite groups, but also witnesses the evolutionary development of concepts that form a basis for current investigations. This is accomplished by providing a thread that permits a natural flow from one concept to another rather than compartmentalizing. Operators on sets and groups are introduced early and used effectively throughout. The bibliography provides excellent supplemental support...The text is tight; there is no fluff. The format builds on concepts essential for later expansion and associated reading. On occasion, results are stated without proof; continuity is maintained. Several proofs are provided free of representation theory on which the originals were based. More generally the proofs are direct, perhaps at times brief. The focus is on the underlying structural components, with selected details left to the reader. As a result the reader develops the maturity required for approaching the literature with confidence. The first eight chapters have an abundance of exercises, not prorated, and some of the more challenging are addressed later in the text. Due to the nature of the material, fewer exercises appear in the remaining chapters." (H. Bechtell, Mathematical Reviews)