# Is there a list of all possible Super-Poincaré algebras up to 11D and their physical supermultiplet representations?

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From looking around it seems like there are

- In each dimension (greater than 1, 2, or maybe 3*) essentially a finite number of possible central extensions of the Super-Poincaré algebra (of various N or (N,M) extended supersymmetry) up to continuous parameters that don't essentially change the algebra (except maybe at special values defined by at most a finite number of algebraic relationships between the central charges Edit: I realized that the lie superalgebra doesn't actually encode any information about the central charges other than that they are non-zero and commute, so any relationships betwen them would be in the representation, not the algebra, I think).
- For each Super-Poincaré algebra with central extension a finite number of supermultiplet representations that are non-negative mass squared and do not contain spins greater than 2.

The classification of the central extensions is certainly non-trivial and because of various kinds of short multiplets the categorization of the physically relevant irreducible supermultiplets is possibly non-tivial.

It seems that because of the eccentricities of lower dimension Lorentz groups that the set of possibilities is very irregular, but because everything is finite it feels like a complete list could be enumerated, perhaps by computer, but I can't find anything even approaching it.

*I know that in lower dimensions there are more possibilities for supersymmetry because of anyons and similar phenomena. I wouldn't be surprised if below a certain dimension it becomes infinitely more complicated, but I don't know if and where that happens.

edited Aug 13, 2015

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