Obtaining the reduced incidence algebra as a matrix algebra

asked 2023-08-15 12:59:06 +0200

klaaa gravatar image

updated 2023-08-15 13:00:09 +0200

I want to use Sage to give me the reduced incidence algebra of a poset P as a finite dimensional algebra generated by matrices, that I can use to input this algebra into GAP.

Question: How can I obtain a list of matrices that generate a finite dimensional algebra using Sage? A multiplication table would also be helpful and might be used to obtain the algebra in GAP.

Here how to use GAP to get an algebra generated by matrices:


Here an example how to get the reduced incidence algebra using Sage:

P = posets.TamariLattice(n)

I = P.incidence_algebra(QQ)


I found the command "table()" (see http://sporadic.stanford.edu/referenc... ) but it seems to not work to give me the matrices that generated the reduced incidence algebra here.

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