This volume is based on lectures on division algebras given at a conference held at Colorado State University. Although division algebras are a very classical object, this book presents this "classical" material in a new way, highlighting current approaches and new theorems, and illuminating the connections with a variety of areas in mathematics.

Readership

Graduate students and research mathematicians working in algebra, especially in theory of fields.

Reviews

"A useful survey of the present state of the subject, going well beyond most other texts in this field."

-- Zentralblatt MATH

Table of Contents

• Introduction
• A division algebra is a central simple algebra
• Azumaya algebras at the generic point
• The Brauer group
• Form of matrices
• Torsion question
• Galois extensions
• Crossed products and cohomology
• Corestriction
• Orders and regular domains
• Ramification
• Specialization and lifting
• Lattice methods
• Brauer Severi varieties
• Generic division algebra
• Bibliography