Symmetries of M-theory and free Lie superalgebras

Abstract

We study systematically various extensions of the Poincaré 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 Poincaré 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.

36 pages. v2: References added, JHEP version

References in corpus (11)

• Very Special Relativity
• E(11) and the Embedding Tensor
• String Solitons and T-duality
• Generalized cosmological term from Maxwell symmetries
• Non-Relativistic Maxwell Chern-Simons Gravity
• On the Maxwell supergravity and flat limit in 2+1 dimensions
• Generalized Chern-Simons higher-spin gravity theories in three dimensions
• Confined dynamical systems with Carroll or Galilei symmetries
• Hidden Role of Maxwell Superalgebras in the Free Differential Algebras of D=4 and D=11 Supergravity
• Local E(11)
• Forms and algebras in (half-)maximal supergravity theories

Cited by in corpus (6)

• Non-Relativistic Gravity Theory based on an Enlargement of the Extended Bargmann Algebra
• Galilean free Lie algebras
• On the supersymmetric extension of asymptotic symmetries in three spacetime dimensions
• Exploring the geometry of supersymmetric double field theory
• Type II Double Field Theory in Superspace
• The M-algebra completes the hierarchy of Super-Exceptional Tangent Spaces