Seminarium KMMF "Teoria Dwoistości"

Super Lie groups arise as a natural generalisation of classical Lie groups within the framework of supergeometry, playing a fundamental role in various areas of mathematical physics, including supersymmetric field theories and supergravity. By definition, a super Lie group is a group object in the category of supermanifolds, and as such, its structure is encoded in terms of sheaves of superalgebras. However, the direct approach to defining and working with super Lie groups via morphisms of sheaves is not convenient for applications in physical theories. To address this problem, the notion of super Harish-Chandra pairs (sHCp) was introduced. A super Harish-Chandra pair (sHCp) consists of a Lie group together with a Lie superalgebra satisfying certain compatibility conditions. In this talk, I will present two approaches to proving the equivalence of categories between super Lie groups and super Harish-Chandra pairs.