BIREP – Representations of finite dimensional algebras at Bielefeld

As part of my PhD studies, there are always bits of code coming up which might be useful for others to use. In particular, some functions for quantum cluster algebras (compatible matrix pairs) are available below.

Please note that all of the code below is work-in-progress and might contain errors and is definitely not written to optimise speed or memory consumption.

After loading these function, we can now compute mutation sequences of compatible matrix pairs:

Functions for green mutation sequences, their Hasse diagrams and more.

Let us showcase the usage of greenLattice by constructing the Tamari poset in the case A_3:

In order to construct a plot of the poset, we produce the heights of the vertices in the lattice as follows:

Note that all cells with an 'Evaluate'-button underneath can be altered - feel free to test the functions on (small enough) skew-symmetrisable matrices of your own choosing. Please feel free to contact me for comments and/or questions.