Notes

• The Kostant-Kirillov Structure on Coadjoint Orbits 

This note was written during my first year of the mater course,  it aims at giving a brief introduction to the symplectic structure on a coadjoint orbit of a Lie algebra (Kostant-Kirillov structure),  and use this to give a symplectic reduction on a certain smooth manifold (Marsden-Weinstein reduction).

• A short note for counting extensions of quiver representations

This note was written during my study of Hall algebras. With A2 type quiver keeping in mind as an example, we use basic linear algebra to count the extensions of quiver (without relations) representations, and then we give a definition of Hall algebra and study it on A2 type quiver.