Question: Lie Algebra calculations


I have a lie algebra, e.g. sl2 or sl3. Elements of these algebra may look like  Qs, where x indicates a Generator of the lie algebra and 's' is a further index. On this latter index there are conditions, for example:

For all x and s with s>1: Qs = 0.

In addition, under the lie algebra commutation relations, 's' behaves for example as:

[ Qs, Qr] = Qs+r.


Now I have to calculate products of these Qs - ex. Qr Qt....Qu - by respecting the commutation relations and the conditions.

I don't know, how I could realize this in Maple? Thanks for any suggestions.




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