Edited By: Jeffrey Bergen; Stefan Catoiu; William Chin

Hopf Algebras

Lecture Notes In Pure and Applied Mathematics Volume: 237
Book | Print Published: 01/01/2004
Print ISBN: 0-8247-5566-9

Description

This volume publishes key proceedings from the recent International Conference on Hopf Algebras held at DePaul University, Chicago, Illinois. With contributions from leading researchers in the field representing North and South America, Europe, and Asia, this outstanding collection deals with current topics ranging from categories of infinitesimal Hopf modules and bimodules to the construction of a Hopf algebraic Morita invariant.

Table of Contents

Infinitesimal Bialgebras, Pre-Lie and Dendriform Algebras
Marcelo Aguiar
Some Remarks on Nichols Algebras
Nicolas Andruskiewitsch
The Coradical of the Dual of a Lifting of a Quantum Plane
Georgia Benkart and Sarah Witherspoon
W New Proof of the Skolem-Noether Theorem
Jeffrey Bergen
Projectivity of a Relative Hopf Module over the Subring of Coinvariants
S. Caenepeel and T. Guedenon
A Brief Introduction to Coalgebra Representation Theory
William Chin
Some Examples of Integrals for Bialgebras
S. Dascalescu
Bi-Frobenius Algebras and Group-Like Algebras
Yukio Doi
Bialgebras and Realizations
R.. L. Grossman and R. G. Larson
Relatively Free Coalgebras
Mikhail Kochetov
Example of Almost Commutative Hopf Algebras Which are not Coquasitriangular
Akira Masuoka
Hopf Algebras of Dimension p2
Siu-Hung Ng
Support Cones for Infinitesimal Group Schemes
Julia Pevtsova
Colagebras from Formulas
Serban Raianu
Fourier Theory for Coalgebras, Bicointegrals and Injectivity for Bicomodules
Walter Ricardo Ferrer Santos
Notes on the Classification of Hopf Algebras of Dimension pq
Mitsuhiro Takeuchi.

Edited By: Alberto Facchini; Evan Houston; Luigi Salce

Rings, Modules, Algebras, and Abelian Groups

Lecture Notes In Pure and Applied Mathematics Volume: 236

Book | Print Published: 01/01/2004
Print ISBN: 0-8247-4807-7

Description

Surveying the most influential developments in the field, this reference reviews the latest research on Abelian groups, algebras and their representations, commutative rings, module and ring theory, and topological algebraic structures?providing more than 600 current references and 570 display equations for further exploration of the topic.

Table of Contents

PARTIAL CONTENTS

Additives Galois Theory of Modules
R. Abraham and P. Schultz
Finitely Generated and Cogenerated QD Groups
U. Albrecht and B. Wickless
Direct Limits of Modules of Finite Projective Dimension
L. Angeleri Hugel and J. Trlifaj
Classification of a Class of Almost Completely Decomposable Groups
E. Blagoveshchenskaya
A Polynomial Ring Sampler
J. W. Brewer
The Picard Group of the Ring of Integer-valued Polynomials on a Valuation Domain
J-L. Chabert
A Note on Cotilting Modules and Generalized Morita Duality
R. R. Colby, R. Colpi, and K. R. Fuller
Dualities Induced by Cotilting Bimodules
R. Colpi
Symmetries and Asymmetries for Cotilting Bimodules
G DfEste
A Constructive Solution to the Base Change Decomposition Problem in B(1)-groups
C. De Vivo and C. Metilli
On a Property of the Adele Ring of the Rationals
D. Dikranjan and U. Zannier
On a Strong Going-between, Going-down, and their Universalizations
D.E. Dobbs and G. Picavet
Factorization of Divosorial Ideals in a Generalized Krull Domain
S. El Baghdadi
Divisorial Multiplication Rings
J. Escoriza and B. Torrecillas
Global Deformations of Lie Algebras
A. Fialowski

Edited by Jed Z. Buchwald and I. Bernard Cohen

Isaac Newton's Natural Philosophy

March 2004
ISBN 0-262-52425-2
6 x 9, 376 pp., 49 illus.
(PAPER)

Newton studies have undergone radical changes in the last half-century as more of his work has been uncovered and more details of his life and intellectual context have come to light. This volume singles out two strands in recent Newton studies: the intellectual background to Newton's scientific thought and both specific and general aspects of his technical science. The essays make new claims concerning Newton's mathematical methods, experimental investigations, and motivations, as well as the effect that his long presence had on science in England.

The book is divided into two parts. The essays in part I shed new light on Newton's motivations and the sources of his method. The essays in part II explore Newton's mathematical philosophy and his development of rational mechanics and celestial dynamics. An appendix includes the last paper by Newton biographer Richard W. Westfall, examining some of the ways that mathematics came to be used in the age of Newton in pursuits and domains other than theoretical or rational mechanics.

Olivier Faugeras and Quang-Tuan Luong

The Geometry of Multiple Images
The Laws That Govern the Formation of Multiple Images of a Scene and Some of Their Applications

March 2004
ISBN 0-262-56204-9
8 x 9, 646 pp., 230 illus.
(PAPER)

Over the last forty years, researchers have made great strides in elucidating the laws of image formation, processing, and understanding by animals, humans, and machines. This book describes the state of knowledge in one subarea of vision, the geometric laws that relate different views of a scene. Geometry, one of the oldest branches of mathematics, is the natural language for describing three-dimensional shapes and spatial relations. Projective geometry, the geometry that best models image formation, provides a unified framework for thinking about many geometric problems relevant to vision. The book formalizes and analyzes the relations between multiple views of a scene from the perspective of various types of geometries. A key feature is that it considers Euclidean and affine geometries as special cases of projective geometry.

Images play a prominent role in computer communications. Producers and users of images, in particular three-dimensional images, require a framework for stating and solving problems. The book offers a number of conceptual tools and theoretical results useful for the design of machine vision algorithms. It also illustrates these tools and results with many examples of real applications.

Peter Pesic

Abel's Proof
An Essay on the Sources and Meaning of Mathematical Unsolvability

April 2004
ISBN 0-262-66182-9
5 3/8 x 8, 216 pp., 46 illus.
(PAPER)

In 1824 a young Norwegian named Niels Henrik Abel proved conclusively that algebraic equations of the fifth order are not solvable in radicals. In this book Peter Pesic shows what an important event this was in the history of thought. He also presents it as a remarkable human story. Abel was twenty-one when he self-published his proof, and he died five years later, poor and depressed, just before the proof started to receive wide acclaim. Abel's attempts to reach out to the mathematical elite of the day had been spurned, and he was unable to find a position that would allow him to work in peace and marry his fiancee.

But Pesic's story begins long before Abel and continues to the present day, for Abel's proof changed how we think about mathematics and its relation to the "real" world. Starting with the Greeks, who invented the idea of mathematical proof, Pesic shows how mathematics found its sources in the real world (the shapes of things, the accounting needs of merchants) and then reached beyond those sources toward something more universal. The Pythagoreans' attempts to deal with irrational numbers foreshadowed the slow emergence of abstract mathematics. Pesic focuses on the contested development of algebra--which even Newton resisted--and the gradual acceptance of the usefulness and perhaps even beauty of abstractions that seem to invoke realities with dimensions outside human experience. Pesic tells this story as a history of ideas, with mathematical details incorporated in boxes. The book also includes a new annotated translation of Abel's original proof.