Books by Anthony W. Knapp

* Presents a comprehensive treatment with a global view of the subject* Rich in examples, problems with hints, and solutions, the book makes a welcome addition to the library of every mathematician

This book offers a systematic treatment--the first in book form--of the development and use of cohomological induction to construct unitary representations. George Mackey introduced induction in 1950 as a real analysis construction for passing from a unitary representation of a closed subgroup of a locally compact group to a unitary representation of the whole group. Later a parallel construction using complex analysis and its associated co-homology theories grew up as a result of work by Borel, Weil, Harish-Chandra, Bott, Langlands, Kostant, and Schmid. Cohomological induction, introduced by Zuckerman, is an algebraic analog that is technically more manageable than the complex-analysis construction and leads to a large repertory of irreducible unitary representations of reductive Lie groups. The book, which is accessible to students beyond the first year of graduate school, will interest mathematicians and physicists who want to learn about and take advantage of the algebraic side of the representation theory of Lie groups. Cohomological Induction and Unitary Representations develops the necessary background in representation theory and includes an introductory chapter of motivation, a thorough treatment of the "e;translation principle,"e; and four appendices on algebra and analysis.

Starting with the elementary theory of Lie groups of matrices, this book arrives at the definition, elementary properties, and first applications of cohomological induction. It is based on a one-semester course given at the State University of New York, Stony Brook in fall, 1986.

Systematically develop the concepts and tools that are vital to every mathematician, whether pure or applied, aspiring or establishedA comprehensive treatment with a global view of the subject, emphasizing the connections between real analysis and other branches of mathematicsIncluded throughout are many examples and hundreds of problems, and a separate 55-page section gives hints or complete solutions for most.

An elliptic curve is a particular kind of cubic equation in two variables whose projective solutions form a group. Developing, with many examples, the elementary theory of elliptic curves, this book goes on to the subject of modular forms and the first connections with elliptic curves.

Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Together, the two books give the reader a global view of algebra and its role in mathematics as a whole.