- Date
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Tuesday 17 December 2024, 12.00 -12.30
- Abstract
- Hopf-Galois theory allows for a Galois-theoretic approach to studying potentially non-Galois field extensions $L/K$ by studying situations in which Hopf algebras act on $L/K$ in some natural way. Given a separable but non-normal field extension $L/K$ of degree n with normal closure E, there may be other degree n sub-extensions $L'/K$ of $E/K$ (we say that $L'/K$ is parallel to $L/K$) which can be related to $L/K$ in many different ways. It is then an interesting question to ask whether, given an extension $L/K$ admitting a Hopf-Galois structure, can we say anything about the Hopf-Galois structures on all of the extensions $L'/K$ parallel to $L/K$? This talk will take a first look at answering this question, approaching the problem from a group-theoretical perspective, outlining some interesting results along the way.
