Schreiber M-Algebra and Exceptional Tangent Spaces

an article that we are finalizing at CQTS:

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• Grigorios Giotopoulos, $\;$ Hisham Sati $\;$and$\;$ Urs Schreiber:

  
  

  The M-algebra completes the hierarchy

  of Super-Exceptional Tangent Spaces

  
  

  Physics Letters B, Volume 860, January 2025, 139199

  doi:10.1016/j.physletb.2024.139199

  
  

  download:

  • arXiv:2411.03661

  • pdf

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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 $n = 11$.

Related talks:

• Super-Exceptional Geometry for 11D Supergravity

Related articles:

• Super-Lie-infinity T-Duality and M-Theory

• The Hidden M-Group

• Super-exceptional embedding construction of the M5-brane

• Super-exceptional M5-brane model