This volume is based on the author's lecture courses to algebraists at Munich and at Göteborg. He presents, for the first time in book form, a unified approach from the point of view of Frobenius algebras/extensions to diverse topics, such as Jones' subfactor theory, Hopf algebras and Hopf subalgebras, the Yang-Baxter Equation and 2-dimensional topological quantum field theories.

Other Features:

• Initial steps toward a theory of noncommutative ring extensions.
• Self-contained sections on Azumaya algebras and strongly separable algebras.
• Applications and generalizations of Morita theory and Azumaya algebra due to Hirata and Sugano.

Understanding the text requires no prior background in Frobenius algebras or Hopf algebras. An index and a thorough list of further references are included. There is an appendix giving a brief historical guide to the literature.

Readership

Graduate students and research mathematicians working in algebra and topology.

Reviews

"Presents a unified approach from the point of view of Frobenius algebras' extensions, to diverse topics such as Jones' subfactor theory, Hopf algebras and subalgebras, the Yang-Baxter equation, and two-dimensional topological quantum field theories."

-- SciTech Book News

Table of Contents

• Introduction to Frobenius extensions
• The endomorphism ring theorem
• The Jones polynomial
• Frobenius algebras
• Azumaya algebras
• Hopf algebras over commutative rings
• Hopf subalgebras
• Historical notes
• Bibliography
• Index