The M-algebra completes the hierarchy of Super-Exceptional Tangent Spaces

TL;DR

This paper explores how the M-algebra, related to M-theory symmetries, extends the hierarchy of super-exceptional tangent spaces up to n=11 by combining brane-extended supersymmetry with exceptional duality symmetries.

Contribution

It demonstrates that the local exceptional duality symmetry acts on the M-algebra, extending the hierarchy of super-exceptional tangent spaces beyond n=7 to n=11.

Findings

Extension of super-exceptional tangent space hierarchy to n=11

Integration of brane-rotating symmetry with exceptional duality

Compatibility with known symmetry structures in M-theory

Abstract

The conjectured symmetries of M-theory famously involve (1.) brane-extended super-symmetry (the M-algebra) and (2.) exceptional duality-symmetry (the $\mathfrak{e}_{11}$-algebra); but little attention has been given to their inevitable combination. In this little note, we highlight (by combining results available in the literature) that the $local$ exceptional duality-symmetry (the hyperbolic involutory $\mathfrak{k}_{1,10} \subset \mathfrak{e}_{11}$) acts on the M-algebra, through the "brane-rotating symmetry" $\mathfrak{sl}_{32}$, in a way which extends the known hierarchy of finite-dimensional $n$-exceptional tangent spaces compatibly beyond the traditional bound of $n \leq 7$ all the way to $n = 11$.