I would aim to know the **complete classification of 6 dimensional non-semi simple Lie algebra** (here the dimension stands for the generators; or the dimension $\leq 6$).

In this paper, in page 7, it stated that: "There is **no complete classification** of the six-dimensional real Lie algebras. However, **all nilpotent six-dimensional Lie algebras are known**." I also found this paper: J.Math.Phys. 17 (1976) 986, which lists nilpotent six-dimensional Lie algebras in Table III, p.991.

My question, again, is that: whether **complete classification of 6 dimensional non-semi simple Lie algebra** is known; for both **real/complex non-semi simple** Lie algebra of dimension 6? What is the most complete result? (In which paper/ref can I find a table of their Lie algebra?) Is that Table III a complete or incomplete for all **real/complex non-semi simple** Lie algebra of dimension 6?

Deep appreciation to whom concern and reply. (My question is motivated by a problem in topological field theory.)

no, right?) – Pete L. Clark Dec 28 '13 at 7:18