
Mathematisches Institut der Universität München
 B. Pareigis
Prof. Dr. Bodo Pareigis, Prof. Dr. Julius Wess
Galois theory of inseparable extensions (Galoistheorie inseparabler Erweiterungen)
 Summer semester 2003
 Time: Friday, 2:15 pm
 Room: 132
 Planning session: Friday, February 4, 2003, 1:45 pm, Room 138
 Contents: It is wellknow that a field extension is Galois if
it is finite, normal, and separable. In this case, the Galois
correspondence yields a onetoone correspondence between the subgroups
of the Galois group and the intermediate fields of the field extension.
In the case of purely inseparable field extensions, one can sometimes
also establish a Galois correspondence by working instead of the
automorphism group with different objects. In the case of extensions of
exponent 1, the automorphism groups are replaced by certain Lie
algebras of derivations; in the case of higher exponents one has to
work instead with socalled higher derivations. Derivations and higher
derivations can be understood as elements of a Hopf algebra, so that
all these Galois correspondences can be subsumed under the HopfGalois
theory.
The seminar is addressed at graduate students who have attended the
course
"Algebra I" and now want to extend the knowledge aquired there. As
prerequisites, linear algebra and the foundations of Galois theory are
sufficient.
 Seminar program
