Series: Modern Birkhauser Classics
1st ed. 1993. Corr. 2nd printing 1994. 3rd. printing, 2008, XII, 342 p. 14 illus., Softcover
ISBN: 978-0-8176-4716-2
A Birkhauser book
Due: January 2008
About this textbook
The quantum groups discussed in this book are the quantized enveloping algebras introduced by Drinfeld and Jimbo in 1985, or variations thereof. It is shown that these algebras have natural integral forms which can be specialized at roots of 1 and yield new objects which include quantum versions of the semi-simple groups over fields of positive characteristic. The theory of quantum groups has led to a new, extremely rigid structure, in which the objects of the theory are provided with canonical basis with rather remarkable properties. The book contains an extensive treatment of the theory of canonical bases in the framework of perverse sheaves. The theory developed in the book includes the case of quantum affine enveloping algebras and, more generally, the quantum analogs of the Kac?Moody Lie algebras.
This book will be of interest to mathematicians working in the representation theory of Lie groups and Lie algebras, knot theorists and to theoretical physicists and graduate students. Since large parts of the book are independent of the theory of perverse sheaves, the book could also be used as a text book.
Table of contents
Preface.- The Drinfeld-Jimbo Algebra U.- Geometric Realization of f.- Part III. Kashiwara’s Operators and Applications.- Canonical Basis of U.- Change of Rings.- Braid Group Action.- Index of Notation.- Index of Terminology.
Series: Graduate Texts in Mathematics , Vol. 243
2008, Approx. 476 p. 41 illus., Hardcover
ISBN: 978-0-387-74611-1
Due: January 2008
About this textbook
Covers important topics not covered elsewhere, such as cell trading
Provides an accessible review of general topology
Contains nearly 50 figures
Includes exercises throughout each chapter
Self-contained and suitable for a graduate course on algebraic topology
This book is about the interplay between algebraic topology and the theory of infinite discrete groups. This text is an important contribution to the field of topological and geometric group theory, and it is bound to become a standard reference in the field. To keep the length reasonable and the focus clear, the author assumes the reader knows or can easily learn the necessary algebra, but wants to see the topology done in detail.
The central theme of the book is the theory of ends. Here the author adopts a new algebraic approach which is geometric in spirit. While the beginning chapters cover standard topics from a 1st year algebraic topology course, the author has also included material which isn't covered in other textbooks, such as cell trading. The early material could be used for a graduate level course on algebraic topology. The latter material will be of interest to group theorists who would like to know more about the topological side of their subject, as well as manifold topologists looking for basic material on proper homotopy and finite homology.
Unique topics include: CW complexes; cellular homology; fundamental group theory; basic homotopy theory; many elementary ideas about manifolds and piecewise linear methods; algebraic topology as applied to finiteness properties and dimension of groups.
Table of contents
Preface.- CW Complexes and Homotopy.- Cellular Homology.- Fundamental Group and Tietze Transformations.- Some Techniques In Homotopy Theory.- Elementary Geometric Topology.- The Borel Construction and Bass-Serre Theory.- Topological Finiteness Properties and Dimension of Groups.- Homological Finitenes Properties of Groups.- Finiteness Properties of Some Important Groups.- Locally Finite CW Complexes and Proper Homotopy.- Locally Finite Homology.- Cohomology of CW Complexes.- Cohomology of Groups and Ends of Covering Spaces.- Filtered Ends of Pairs of Groups.- Poincare Duality in Manifolds and Groups.- The Fundamental Group at Infinity.- Higher Homotopy Theory of Groups.- Three Essays.- References.- Index
Series: Graduate Texts in Mathematics , Preliminary entry 245
2008, Approx. 235 p., Hardcover
ISBN: 978-0-387-74714-9
Due: January 2008
About this textbook
Covers vast majority of the material needed for a beginning graduate level course on complex analysis
Elegant and economical treatment of complex analysis
Provides many ways of understanding the concept of analyticity
Material of interest to computer scientists, physicists and engineers
This book organizes the basic material of complex analysis in a unique manner.
The first part of the book is a study of the many equivalent ways of understanding the concept of analyticity. The many ways of formulating the concept of an analytic function are summarized in what we term the Fundamental Theorem for functions of a complex variable. The organization of these conditions into a single unifying theorem is a hallmark of Bers's mathematical style with an emphasis on clarity and elegance. Here it provides a conceptual framework for results that are highly technical and often computational. The framework comes from an insight that, once articulated, will drive the subsequent mathematics and lead to new results.
In the second part, the text proceeds to a leisurely exploration of interesting ramifications of the main concepts.
The book covers most, if not all, of the material contained in Bers’s courses on first year complex analysis. In addition, topics of current interest such as zeros of holomorphic functions and the connection between hyperbolic geometry and complex analysis are explored.
The organization of material in this book allows for an elegant and economical treatment of many important topics.
Table of contents
Preface.- Standard notation and commonly used symbols.- The fundamental theorem in complex function theory.- Foundations.- Power series.- The cauchy theory-a fundamental theorem.- The cauchy theory-key consequences.- Cauchy theory: local behavior and singularities of holomorphic functions.- Sequences and series of holomorphic functions.- Conformal equivalence.- Harmonic functions.- Zeros of holomorphic functions.- Bibliographical notes.- Bibliography.- Index
2008, Approx. 750 p., Hardcover
ISBN: 978-3-540-71296-1
Due: April 2008
About this book
Editors very well known in their area of research
Many outstanding contributors
Preamble by Nobel prize winner Robert F. Engle
The Handbook of Financial Time Series gives an up-to-date overview of the field and covers all relevant topics both from a statistical and an econometrical point of view.
Experts present among others various aspects of the important GARCH and Stochastic Volatility classes, like for example distribution properties, estimation, forecasting and extreme value theory. Moreover, since processes in continuous time and cointegration play a very essential role in financial modelling, both areas are addressed in detail. Finally, recent developments in nonparametric methods, copulas, structural breaks, high frequency data and many more topics are included in the handbook.
Many outstanding authors have contributed to this encyclopaedia, making the volume an excellent source of reference for scientists and researchers working in the field of financial time series.
Table of contentsIntroduction - GARCH-Modelling - Stochastic Volatility Modelling - Cointegration - Continuous Time Processes - Miscellanea