What does ⋉ mean? It's simple if you know spacetime translations!
- hyaline chen
- Nov 19
- 1 min read
In this post, I want to introduce the notion of a semidirect product, "⋉", in abstract algebra, from the eyes of a physicist, through the familiar Poincare group of symmetries of a Lorentz spacetime.
When I first learnt about semi direct product, these seemed entirely mysterious. Why are we defining them this way? This is the question I try to answer in this post.
So Semidirect products are introduced precisely to capture structures of groups such as that of symmetries of the flat spacetime - rotating and translating doesn't commute with each other, and compositions of these actions have nontrivial structures not captured by a direct sum, but a semidirect product.
Very simple!
(Thanks to Kye for mentioning this)
Comments