B Is the 10 Dimensional Poincaré Group a Coincidence?

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TL;DR
The Poincaré group and M-theory both have 10 dimensions
Is this a coincidence?
 
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Paige_Turner said:
Summary:: The Poincaré group and M-theory both have 10 dimensions

Is this a coincidence?
Yes. And there isn't even a defined single dimension for an M-theory, since there are several different concepts unified in M-theory. In any case, M-theory generalizes string theories, which involve super Lie algebras. The Poincaré group has a classical Lie algebra and moreover isn't semisimple.
 


Well, it depends on what you're referring to as a coincidence. Can you provide more context or information? Without more details, it's difficult to say whether or not something is a coincidence.
 
We all know the definition of n-dimensional topological manifold uses open sets and homeomorphisms onto the image as open set in ##\mathbb R^n##. It should be possible to reformulate the definition of n-dimensional topological manifold using closed sets on the manifold's topology and on ##\mathbb R^n## ? I'm positive for this. Perhaps the definition of smooth manifold would be problematic, though.

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