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Explore the intricacies of extensions of affine algebra Vertex Operator Algebras (VOAs) in this 54-minute lecture by Terry Gannon, presented at the Workshop on Quantum Symmetries at the Centre de recherches mathématiques (CRM). Delve into the world of rational VOAs, focusing on V(g,k) associated with simple Lie algebras at positive integer levels. Discover how to identify all finite-index extensions of V(g,k) and learn about the bound K(g) that determines when extensions are by simple currents. Examine the complete classification of extensions for all Lie algebras of rank less than 7 at all levels, addressing a longstanding question in quantum subgroup theory dating back to Witten's work in the 1980s. Gain insights into the module category classification for C(g,k) and understand the significance of this research in the context of quantum symmetries and tensor categories.
