Symmetries of M-theory and free Lie superalgebras

TL;DR

This paper explores the universal extension of the Poincaré superalgebra via free Lie superalgebras, revealing connections to Borcherds superalgebras and implications for M-theory symmetries.

Contribution

It systematically studies free Lie superalgebras as extensions of the Poincaré superalgebra and relates them to known algebraic structures in M-theory.

Findings

Identifies free Lie superalgebras as universal extensions of Poincaré superalgebra.

Shows how quotients relate to Borcherds superalgebras.

Provides new perspectives on exotic branes and symmetries in M-theory.

Abstract

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. The ideas put forward also offer some new angles on exotic branes and extended symmetry structures in M-theory.