Symmetries of M-theory and free Lie superalgebras

Understand

We study systematically various extensions of the Poincar\'e superalgebra.

• The most general structure starting from a set of spinorial supercharges $Q_\alpha$ is a free Lie superalgebra that we discuss in detail.
• We explain how this universal extension of the Poincar\'e superalgebra gives rise to many other algebras as quotients, some of which have appeared previously in various places in the literature.
• In particular, we show how some quotients can be very neatly related to Borcherds superalgebras.