Research Focus
With the exception of my early work on module theory, homological algebra, and abelian groups, the enduring theme of my mathematical interests and research has been the Galois theory of rings and fields, and variations of these theories in which the role of the classical Galois group is played by some related algebraic structure such as a restricted Lie algebra, group scheme, Hopf algebra, or groupoid. This work impinges upon and utilizes techniques from other areas in which I also have strong interests, such as category theory and homological algebra, group theory, group schemes and Hopf algebras, representation theory, algebraic K-theory, and algebraic number theory.
Following a period in my career in which the main focus of my research was the Galois module structure of algebraic integers, I have returned to investigations in pure algebra; these involve primarily Hopf algebras (especially quantum groups and Tannakian reconstruction) and, more recently, finite groups (especially the structure of p-groups).
Publications
- Galois theory and Galois cohomology of commutative rings (with D. K. Harrison and A. Rosenberg), Amer. Math. Soc. Memoir 52 (1965).
- Hopf algebras and Galois theory (with M. E. Sweedler), Lecture Notes in Math 97, Springer-Verlag, 1969.
- Infinitesimal group scheme actions on finite field extensions, Amer. J. Math. 98 (1976), 441–480.
- Ramification invariants and torsion Galois module structure in number fields, J. Algebra 91 (1984), 207–257.
- Generalized Hopf Modules for bimonads (with Marcelo Aguiar). Theory and Applications of Categories, Vol. 27 (2013), No. 13, 263-326.