Section
Supergeometry
Super linear algebra, smooth real supermanifolds, Lie supergroups, and their mathematical-physics enrichments.
Core idea
This section uses finite-dimensional smooth real Berezin–Leites/Kostant supermanifolds and even morphisms unless stated otherwise. Complex-analytic, algebraic, DeWitt, and Rogers models are related theories, not automatic synonyms.
Super linear algebra
- Super vector space
- Parity shift
- Category of super vector spaces
- Koszul sign rule
- Super internal Hom
- Superalgebra
- Supercommutator
- Supercommutative algebra
- Supermodule
- Symmetric algebra of a super vector space
- Lie superalgebra
- Representation of a Lie superalgebra
- Universal enveloping algebra of a Lie superalgebra
- Super PBW theorem
Superspaces and supermanifolds
- Superspace
- Superdomain
- Supermanifold
- Split supermanifold
- Batchelor theorem
- Functor of points of a supermanifold
Lie theory
- Lie supergroup
- Lie superalgebra of a Lie supergroup
- Super Harish–Chandra pair
- Equivalence of Lie supergroups and super Harish–Chandra pairs
Supersymmetry geometry
- Supertranslation algebra
- Poincaré algebra
- Super-Poincaré algebra
- Super-Minkowski space
- Supertranslation distribution
References
- V. S. Varadarajan, Supersymmetry for Mathematicians: An Introduction, Courant Lecture Notes 11, American Mathematical Society, 2004. Publisher record.
- C. Carmeli, L. Caston, and R. Fioresi, Mathematical Foundations of Supersymmetry, EMS, 2011. Publisher record.