Monday 11th of November 2024, 13:30-14:30 in HFML0220
Maxime Wybouw
Chain complexes and Korzul duality
Homology theory is a powerful way to compute and encode invariants of an object. We will start with the homology of modules, which uses a resolution to obtain desired invariants like the Ext-groups. We will see how to extend this framework to also include homology of algebras such as Lie and associative algebras. A powerful tool here is the idea of Koszul duality, which gives a minimal resolution of your algebraic structure. The end goal is to give an idea of how Lie algebras are Koszul dual to commutative algebras. One application of this was the recent proof of Campos, Petersen, Robert-Nicoud and Wierstra that a nilpotent Lie algebra is determined by its enveloping algebra *as an associative algebra*.