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.
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 DfEste
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
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.
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.
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.