My field of research is in the area known as Hopf-Galois Theory which is a generalization of the classical Galois theory for fields.

In this setting one can consider a separable extension (which may not be Galois in the usual sense) as being Hopf-Galois where instead of a group acting on the extension, one has a Hopf algebra which acts. Note that a classical Galois extension L/K with G=Gal(L/K) is also Hopf-Galois in a very natural way under the action of the Hopf algebra H=K[G].

The work of Greither and Pareigis showed how to classify and enumerate such extensions by looking at certain permutation groups.

In broad terms Hopf-Galois theory can be viewed as an aspect of Galois Module Theory.

Publications

[1] Group Rings and Hopf Galois Theory in Maple in Maple V: Mathematics and Its Application, Proceedings of the the Maple Summer Workshop and Symposium, Rensselear Polytechnic Institute, Troy, New York, August 9-13, 1994, Robert J. Lopez, Editor, Birkhaü ser Boston, 1994.

[2] Classification of the Hopf Galois Structures on Prime Power Radical Extensions, J. Algebra, 207 (1998), 525-546

[3] (with D. Replogle) Computation of Several Cyclotomic Swan Subgroups, Math. Comp., 71 (2002),343-348

[4] (with D. Replogle) Cyclotomic Swan Subgroups and Primitive Roots, Finite Fields and Their Applications,11 (2005),655-666

[5] Groups of Order 4p, Twisted Wreath Products and Hopf-Galois Theory J. Algebra, 314 (2007), 42-74.

Presentations

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