Hopf Algebras and Galois Module Theory

Lindsay N. Childs, University at Albany, NY. Cornelius Greither, Universitat der Bundeswehr Munchen, Neubiberg, Germany. Kevin P. Keating, University of Florida, Gainesville, FL. Alan Koch, Agnes Scott College, Decatur, GA. Timothy Kohl, Boston University, MA. Paul J. Truman, Keele University, Staffordshire, United Kingdom. Robert G. Underwood, Auburn University at Montgomery, AL.

Introduction: What is this book about? Hopf-Galois extensions: Hopf-Galois structures on Galois extensions of fields, regular subgroups, and skew braces (Non)-existence results on Hopf-Galois structures Hopf-Galois structures arising from fixed point free pairs of homomorphisms Quantitative results Enumeration of Hopf-Galois structures on Galois extenion of degree $mp$ On the Galois correspondence for Hopf-Galois structures Normality in Hopf-Galois extensions Descent theory, and the structure of Hopf algebras acting on separable field extensions Hopf-Galois actions on purely inseparable extensions Hopf-Galois module theory: Hopf-Galois module theory Hopf orders in group rings Ramification theory for separable extensions of local fields Stable and semistable Hopf-Galois extensions Hopf-Galois scaffolds Bibliography Index