Generalized Pauli matrices? (and Gell-Mann matrices)

[F. B.]

What about generalizing the Pauli matrices to any dimension?

Pauli matrices generate the algebra of SU(2), Gell-Mann matrices the one of SU(3).

Wikipedia has an article about a generalization for SU(N): Generalizations_of_Pauli_matrices

There is currently an msigma( ) function in sympy.physics, yielding Pauli matrices. It should be easy to port Wikipedia's generalization to N-dimensions. What do you think?

[Aaron Meurer]

Sounds good to me. 

Aaron Meurer

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[Stefan Krastanov]

There are already a few prototype-stage proposals about this that
might give you an idea how to proceed:

- Pernici employed abstract tensors for this here
https://github.com/sympy/sympy/pull/1699
It is unmerged. Search for "gamma matrices" in the pull
request description. Only a small part of this pull request
deals with gamma matrices, so do not be scared by the
fact that it is more than 3000 lines.

- I hacked together some simplistic implementation here
https://github.com/sympy/sympy/pull/1635

- There is a GSoC proposal, that if accepted can implement
a lot of the Lie Groups/Algebras theory related to SU(n)

In any case, if this is to be useful for the `quantum` module, it
would have to interface with its methods for determining a base,
evaluating operations, etc. This is almost a whole new CAS within
SymPy.