Category Archives: group-theory

## Highlights in Linear Algebraic Groups 10: G/B is Projective

In Highlights 9 of this series, we showed that for an algebraic group $G$ and a closed subgroup $H\subseteq G$, we can always choose a representation $G\to\rm{GL}(V)$ with a line $L\subseteq V$ whose stabiliser is $H$. In turn, this allows us to identify the quotient $G/H$ with the orbit […]

## Dihedral Groups and Automorphisms, Part 1

Welcome to the second two-post series on AZC! The evil secret plot of this series is to make group cohomology seem interesting for those who have not seen much group cohomology. To do this, we will dissect the dihedral group, which most math majors have probably seen as undergrads. However, to be thorough, the first […]