Galois theory of inseparable extensions
- Summer semester 2003
- Time: Friday, 2:15 pm
- Room: 132
- Planning session: Friday, February 4, 2003, 1:45 pm, Room 138
It is well-know that a field extension is Galois if it is finite, normal, and separable. In this case, the Galois correspondence yields a one-to-one 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 so-called 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 Hopf-Galois 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 (german, dvi)