The Theory of Fusion Systems: An Algebraic Approach

ISBN-13: 9781107005969 / Angielski / Twarda / 2011 / 384 str.

David A Craven

Opis

Fusion systems are a recent development in finite group theory and sit at the intersection of algebra and topology. This book is the first to deal comprehensively with this new and expanding field, taking the reader from the basics of the theory right to the state of the art. Three motivational chapters, indicating the interaction of fusion and fusion systems in group theory, representation theory and topology are followed by six chapters that explore the theory of fusion systems themselves. Starting with the basic definitions, the topics covered include: weakly normal and normal subsystems; morphisms and quotients; saturation theorems; results about control of fusion; and the local theory of fusion systems. At the end there is also a discussion of exotic fusion systems. Designed for use as a text and reference work, this book is suitable for graduate students and experts alike.

Recenzje

"This very welcome book originates from a workshop on fusion systems held at the University of Birmingham in 2007 and is one of the first two texts on the subject, appearing at approximately the same time... The book serves as an excellent introduction to the subject and a guide to up to the cutting edget of current research."
Charles W. Eaton, Mathematical Reviews

Spis treści

Preface; Part I. Motivation: 1. Fusion in finite groups; 2. Fusion in representation theory; 3. Fusion in topology; Part II. The Theory: 4. Fusion systems; 5. Weakly normal subsystems, quotients, and morphisms; 6. Proving saturation; 7. Control in fusion systems; 8. Local theory of fusion systems; 9. Exotic fusion systems; References; Index of notation; Index.