Division algebras and supersymmetry

Abstract: In this introduction suitable for graduate students, we use the four normed division algebras to introduce some basic elements of supersymmetry. Namely, from the four normed division algebras (the real numbers, the complex numbers, the quaternions and the octonions), a uniform construction yields the super-Minkowski spacetimes on which the classical superstring can be defined. We review this construction and show how the alternativity of the division algebras allows us to define a class in the third cohomology on super-Minkowski spacetime, which in turn allows us to write the classical action of the superstring. In conclusion, we describe how this degree three class defines a "higher" algebraic structure.