Lie Groups #4 - Homogeneous Spaces

This is a very brief introduction to the vastly important topic of homogeneous spaces, which are symmetric geometries formed using an equivalence class of Lie groups (sometimes called Klein geometries). We realise symmetric spaces in this way by forming a quotient space with a Lie group that contains a smaller Lie group (known as the stabiliser subgroup, although I forgot to mention this terminology!)

I mention how all N-dimensional spheres are formed using the relation SO(N+1)/SO(N) ~ S^N, in future videos we will see other examples of homogeneous spaces, for example the Minkowski spacetime (ISO(1, d)/SO(1,d))

Видео Lie Groups #4 - Homogeneous Spaces канала WHYBmaths