📁Categories of finite-dimensional modules, Lie algebras, homological algebra

The BBG category \(\mathcal{O}\)

Supervisor: Alessio Cipriani

Description

Given a finite-dimensional semisimple complex Lie algebra \( \mathfrak{g} \), the Bernstein–Gelfand–Gelfand category \( \mathcal O \) is the full subcategory of \( \mathfrak{g} \)-modules which satisfies some finiteness conditions. This category turns out to be a highest weight category with connection to Kazhdan–Lusztig theory and Schubert varieties.