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Given a finite list W of nilpotent matrices in Sage. How can I obtain the Lie algebra L generated by those matrices in W? And how can I find the vector space dimension and test whether L is simple using Sage? I googled a bit and found the command:

L=LieAlgebra(associative=[M, N])

here [M,N] is a list of two matrices. It works to give me a Lie algebra, but then nearly no command works to find the dimension of L (I guess it is somehow in the wrong category?)

Obtaining a Lie algebra from a list of matrices Given a finite list W of nilpotent matrices in Sage. How can I obtain th

Obtaining a Lie algebra from a list of matrices Given a finite list W of nilpotent matrices in Sage. How can I obtain th

Exterior face ring via Sage Let F be a field and let K be a finite simplicial complex, then the face algebra R of K is t

Obtaining Betti numbers in Sage Let $A$ be a commutative finite dimensional $K$-algebra over a field $K$ that is local o

With some help of ChatGPT it seems to work now, see the code below. But there is a problem remaining: The output U does

It seems there is a problem with the multiplication in the exterior algebra.

Thank you. I tried to modify the code but got an error. Here my attempt: def extfacealgbasering(self, base_ring):

Exterior face ring via Sage Let $K$ be a finite simplicial complex, then the face ring of K is the ring $A/I$ where $A$

It might also be useful to have this algebra in Sage, but Im not very experienced with analysing algebras in Sage.

But it might also be useful to have this algebra in Sage, but Im not very experienced with analysing algebras in Sage.

Sage has the needed data on semisimple Lie algebras I think, for example to get a nice basis with known multiplication t

It is about presenting it for QPA. Getting the algebra inside Sage might be not so useful as GAP and QPA have more comma

Obtaining a finite dimensional algebra associated to Lie algebras in QPA Let g be a finite dimensional semisimple Lie al

Obtaining a finite dimensional algebra associated to Lie algebras in QPA Let g be a finite dimensional semisimple Lie al

Obtaining a finite dimensional algebra associated to Lie algebras in QPA Let g be a finite dimensional semisimple Lie al

Thank you very much again! I noted that there is an error for E7: Q = ClusterQuiver(['E',7]) Ts = Q.mutation_class() g

Thank you very much again! A last small question: Is there an easy command to filter out those quivers, which are not ac

Thank you very much. The first way works in the sage online cell, while the second outputs nothing (I dont know why). Bu

Obtaining mutation class of a quiver in Sage with Sage Given a quiver $Q$ of finite mutation class (such as a Dynkin qui

I have a set of variables $x_1,...,x_n$ and $y_1,...,y_m$ for $n,m >=1$.

Now I can build all quadratic monomials of the form $x_i y_j$ and $y_j x_i$ (but we do not have $x_i y_j= y_j x_i$ as we calcualte in the non-commutative polynomial ring). But something like $x_i x_j$ is not allowed as after an $x_i$ there must come an $y_j$ and after an $y_i$ there must come an $x_i$.

Now I want with Sage the list of all possible relations of the form $w_1 \pm w_2 \pm w_3 \cdots$ such that all $w_i$ are different quadratic relations that all start either with a $x_i$ or a $y_j$.

For example for $n=2$ and $m=1$, possible relations are (I hope I did not forget any relation) : $x_1 y_1, x_1 y_1-x_2 y_2, x_1 y_2 + x_2 y_2 , x_2 y_1,y_1 x_1, y_1 x_2, y_1 x_1 - y_1 x_2 , y_1x_1+y_1 x_2$.

I am not sure how to do this in an easy way with Sage, but maybe someone knows a simple trick.

Thanks for any help.