Split Semisimple Groups
Date:
I presented a talk at the UCLA Participating Algebra Seminar on Split Semisimple Groups. Following Chapter 25 of Knus-Merkurjev-Rost-Tignol’s The Book of Involutions, I introduced the definitions of split semisimple groups and their representations. I constructed root systems and proved that every split semisimple admits a central isogeny from a simply connected group and to an adjoint group, and classified the classical groups (type A, B, C, D) via root systems.
Notes are available here.