Algebraic homogeneous spaces

Algebraic homogeneous spaces are mathematical structures that arise in the context of algebraic geometry and representation theory. More specifically, they are typically associated with algebraic groups and their actions on varieties. ### Definition An **algebraic homogeneous space** can be defined in the following way: 1. **Algebraic Group**: Let \( G \) be an algebraic group defined over an algebraically closed field (like the field of complex numbers).