Refine Results
Sort By
From
To
Page 3
Page 3
Linear Algebraic Monoids
The theory of linear algebraic monoids culminates in a coherent blend of algebraic groups, convex geometry, and semigroup theory. The book discusses all the key topics in detail, including classification, orbit structure, representations, universal constructions, and abstract analogues. An explicit cell decomposition is constructed for the wonderful compactification, as is a universal deformation for any semisimple group. A final chapter summarizes important connections with other areas of algebra and geometry. The book will serve as a solid basis for further research. Open problems are discussed as they arise and many useful exercises are included.
Lie Theory Vol.229 : Unitary Representations and Compactifications of Symmetric Spaces
It focuses on two fundamental questions in the theory of semisimple Lie groups: the geometry of Riemannian symmetric spaces and their compactifications; and branching laws for unitary representations, i.e., restricting unitary representations to (typically, but not exclusively, symmetric) subgroups and decomposing the ensuing representations into irreducibles.Ji's introductory chapter motivates the subject of symmetric spaces and their compactifications with carefully selected examples. A discussion of Satake and Furstenberg boundaries and a survey of the geometry of Riemannian symmetric spaces in general provide a good background for the second chapter, namely, the Borel–Ji authoritative treatment of various types of compactifications useful for studying symmetric and locally symmetric spaces. Borel–Ji further examine constructions of Oshima, De Concini, Procesi, and Melrose, which demonstrate the wide applicability of compactification techniques. Kobayashi examines the important subject of branching laws. Important concepts from modern representation theory, such as Harish–Chandra modules, associated varieties, microlocal analysis, derived functor modules, and geometric quantization are introduced. Concrete examples and relevant exercises engage the reader.
Lie theory ; Vol.230 : Harmonic analysis on symmetric spaces, general Plancherel theorems
Van den Ban’s introductory chapter explains the basic setup of a reductive symmetric space along with a careful study of the structure theory, particularly for the ring of invariant differential operators for the relevant class of parabolic subgroups. Advanced topics for the formulation and understanding of the proof are covered, including Eisenstein integrals, regularity theorems, Maass–Selberg relations, and residue calculus for root systems. Schlichtkrull provides a cogent account of the basic ingredients in the harmonic analysis on a symmetric space through the explanation and definition of the Paley–Wiener theorem. Approaching the Plancherel theorem through an alternative viewpoint, the Schwartz space, Delorme bases his discussion and proof on asymptotic expansions of eigenfunctions and the theory of intertwining integrals.
Lie Groups : An Approach through Invariants and Representations
Lie groups has been an increasing area of focus and rich research since the middle of the 20th century. Procesi's masterful approach to Lie groups through invariants and representations gives the reader a comprehensive treatment of the classical groups along with an extensive introduction to a wide range of topics associated with Lie groups: symmetric functions, theory of algebraic forms, Lie algebras, tensor algebra and symmetry, semisimple Lie algebras, algebraic groups, group representations, invariants, Hilbert theory, and binary forms with fields ranging from pure algebra to functional analysis.
Lie Algebras and Algebraic Groups
The theory of Lie algebras and algebraic groups has been an area of active research in the last 50 years. It intervenes in many different areas of mathematics : for example invariant theory, Poisson geometry, harmonic analysis, mathematical physics. The aim of this book is to assemble in a single volume the algebraic aspects of the theory so as to present the foundation of the theory in characteristic zero. Detailed proofs are included and some recent results are discussed in the last chapters. All the prerequisites on commutative algebra and algebraic geometry are included.
Lectures on the Automorphism Groups of Kobayashi-Hyperbolic Manifolds
Presents a coherent exposition of recent results on complete characterization of Kobayashi-hyperbolic manifolds with high-dimensional groups of holomorphic automorphisms. These classification results can be viewed as complex-geometric analogues of those known for Riemannian manifolds with high-dimensional isotropy groups, that were extensively studied in the 1950s-70s. The common feature of the Kobayashi-hyperbolic and Riemannian cases is the properness of the actions of the holomorphic automorphism group and the isometry group on respective manifolds.
Lectures on Symplectic Geometry
Provides a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or extend the reader's understanding.
Learning through Community : Exploring Participatory Practices
A collection of case studies that explore the learning that people do through community engagement. Developed within a network of Canadian researchers and their community partners, it explores learning that is organized by the learners themselves, collectively, rather than as individuals. Reflecting the contributors’ political priorities, the volume begins with groups that are highly marginalized in our society: immigrant women, sex trade workers, senior citizens, garment workers, women doing community economic development, and people who identify with disability and anti-poverty movements.
Lattices and Ordered Algebraic Structures
Lattices and Ordered Algebraic Structures provides a lucid and concise introduction to the basic results concerning the notion of an order. Although as a whole it is mainly intended for beginning postgraduates, the prerequisities are minimal and selected parts can profitably be used to broaden the horizon of the advanced undergraduate. The treatment is modern, with a slant towards recent developments in the theory of residuated lattices and ordered regular semigroups.
L’isomorphisme entre les tours de Lubin-Tate et de Drinfeld = The isomorphism between the Lubin-Tate and Drinfeld towers
This book contains a detailed and complete demonstration of the existence of an equivariate isomorphism between the Lubin-Tate and Drinfeld p-adic turns. The result is established in equal and unequal characteristics. There is also given as an application a proof that the equivariant cohomologies of these two turns are isomorphic, a result which has applications to the study of the local Langlands correspondence. During the proof, reminders and complements are given on the structure of the two preceding moduli spaces, the p-divisible formal groups and the p-adic rigid analytical geometry.
Complex Analysis : In the Spirit of Lipman Bers
In this book, the main focus is the theory of complex-valued functions of a single complex variable. This theory is a prerequisite for the study of many current and rapidly developing areas of mathematics including the theory of several and infinitely many complex variables, the theory of groups, hyperbolic geometry and three-manifolds, and number theory.
Compactifications of Symmetric and Locally Symmetric Spaces
Noncompact symmetric and locally symmetric spaces naturally appear in many mathematical theories, including analysis (representation theory, nonabelian harmonic analysis), number theory (automorphic forms), algebraic geometry (modulae) and algebraic topology (cohomology of discrete groups). In most applications it is necessary to form an appropriate compactification of the space. The literature dealing with such compactifications is vast. The main purpose of this book is to introduce uniform constructions of most of the known compactifications with emphasis on their geometric and topological structures. The book is divided into three parts. Part I studies compactifications of Riemannian symmetric spaces and their arithmetic quotients. Part II is a study of compact smooth manifolds. Part III studies the compactification of locally symmetric spaces.
Compact Lie Groups
This book covers the structure and representation theory of compact Lie groups. The necessary Lie algebra theory is also developed in the text with a streamlined approach focusing on linear Lie groups.
Communicative figurations : Transforming communications in times of deep mediatization
This open access volume is about how to research the influence of our changing media environment. Today, there is not one single medium that is the driving force of change. With the spreading of various technical communication media such as mobile phone and internet platforms, we are confronted with a media manifold of deep mediatization. But how can we investigate its transformative capability? This book answers this question by taking a non-media-centric perspective, researching the various figurations of collectivities and organizations humans are involved in. The first part of the book outlines a fundamental understanding of the changing media environment of deep mediatization and its transformative capacity. The second part focuses on collectivities and movements: communities in the city, critical social movements, maker, online gaming groups and networked groups of young people. The third part moves institutions and organizations into the foreground, discussing the transformation of journalism, religion, politics, and education, whilst the fourth and final part is dedicated to methodologies and perspectives.
Classification des Groupes Algébriques Semi-simples = The Classification of Semi-Simple Algebraic Groups
The third volume of the Collected Works of Claude Chevalley assembles his work on semi-simple algebraic groups contained, for the most part, in the notes of the famous "Sminaire Chevalley" held at the Ecole Normale Suprieure in Paris between 1956 and 1958 and written up by participants of the seminar namely, P. Cartier, A. Grothendieck, R. Lazard and J.L. Verdier. These texts have been entirely reset in TeX for this edition, and edited and annotated by Pierre Cartier. Almost 50 years after the original writing, these texts still constitute a choice reference from which to enter
Classes of Finite Groups
Many group theorists all over the world have been trying in the last twenty-five years to extend and adapt the magnificent methods of the Theory of Finite Soluble Groups to the more ambitious universe of all finite groups. This is a natural progression after the classification of finite simple groups but the achievements in this area are scattered in various papers.Our objectives in this book were to gather, order and examine all this material, including the latest advances made, give a new approach to some classic topics, shed light on some fundamental facts that still remain unpublished and present some new subjects of research in the theory of classes of finite, not necessarily solvable, groups.
Child Protection in England, 1960–2000 : Expertise, Experience, and Emotion
Explores how children, parents, and survivors reshaped the politics of child protection in late twentieth-century England. Activism by these groups, often manifested in small voluntary organisations, drew upon and constructed an expertise grounded in experience and emotion that supported, challenged, and subverted medical, social work, legal, and political authority. New forms of experiential and emotional expertise were manifested in politics – through consultation, voting, and lobbying – but also in the reshaping of everyday life, and in new partnerships formed between voluntary spokespeople and media. While becoming subjects of, and agents in, child protection politics over the late twentieth century, children, parents, and survivors also faced barriers to enacting change, and the book traces how long-standing structural hierarchies, particularly around gender and age, mediated and inhibited the realisation of experiential and emotional expertise.
Care Poverty : When Older People’s Needs Remain Unmet
This book turns the research attention of social policy scholars and long-term care researchers from comparative descriptions of care systems, focusing mostly on expenditures and volumes of long-term care services, to outcomes, and in particular to the question whether older people really receive the support that they need. Without knowledge about which needs and which social groups are currently inadequately covered, it is impossible to guide policy development.
Braid Groups
Braids and braid groups have been at the heart of mathematical development over the last two decades. Braids play an important role in diverse areas of mathematics and theoretical physics. The special beauty of the theory of braids stems from their attractive geometric nature and their close relations to other fundamental geometric objects, such as knots, links, mapping class groups of surfaces, and configuration spaces. In this presentation the authors thoroughly examine various aspects of the theory of braids, starting from basic definitions and then moving to more recent results. The advanced topics cover the Burau and the Lawrence--Krammer--Bigelow representations of the braid groups, the Alexander--Conway and Jones link polynomials, connections with the representation theory of the Iwahori--Hecke algebras, and the Garside structure and orderability of the braid groups.
BioMEMS and biomedical nanotechnology ; Vol. IV : Biomolecular Sensing, Processing and Analysis
This volume contains 18 chapters focused on ‘Biomolecular Sensing, Processing and Analysis’, written by experts in the field of BioMEMS and biomedical nanotechnology. The chapters are groups into three broad categories of Sensors and Materials, Processing and Integrated Systems, and Microfluidics.Prof. Taun Vo-Dinh from Oakridge National Labs begins the Sensors and Materials section by providing a review of biosensors and biochips. This review is followed by an example of mechanical cantilever sensor work described by Prof. Arun Majumdar’s group at UC Berkeley and Prof. Tom Thundat at Oakridge National Laboratory.
