Some Results on Cubic and Higher Order Extensions of the Poincar\'e Algebra

Understand

In these lectures we study some possible higher order (of degree greater than two) extensions of the Poincar\'e algebra.

• We first give some general properties of Lie superalgebras with some emphasis on the supersymmetric extension of the Poincar\'e algebra or Supersymmetry.
• Some general features on the so-called Wess-Zumino model (the simplest field theory invariant under Supersymmetry) are then given.
• We further introduce an additional algebraic structure called Lie algebras of order F, which naturally comprise the concepts of ordinary Lie algebras and superalgebras.