I agree that "abelian" is often uncapitalized, but if that's a sign of respect, why is Gaussian (Gaussian elimination, Gaussian distribution, Gaussian process, etc) almost always capitalized? Or Hilbert space, Poisson distribution, Bernoulli trial, Cartesian coordinates, Euclidean distance?

It seems to me that Abelian goes uncapitalized because few people know about Niels Henrik Abel, and it should properly be capitalized.