This package converts Brauer Graphs into Brauer Graph Algebra in GAP. The prerequisite package for this is QPA (https://www.gap-system.org/Packages/qpa.html). 

The function makeBrauerGraphAlgebra takes in a list containing 3 lists in the following order:

	(1) Vertices := List of names of vertices of the Brauer Graph with their multiplicities (default 1)
	eg. ["v1", ["v2", 1], ["v3", 2]] contains 3 vertices with the third having multiplicity 2 while the others have multiplicity 1. 
	(2) Edges := List of edges where an edge is a list consisting of the name, as well as the name of the two vertices it connects.
	eg. [["e1", "v1", "v3"], ["e2", "v2", "v3"]] is a list of two edges, where the first connects "v1" to "v3" and the second connects "v2" to "v3".
	(3) Orientations := List of ordered edges indexed by vertices. It requires a list for each vertex.
	eg. [["v1", "e1"],["v2", "e2"],["v3", "e2", "e3"]]

Using QPA, it creates a quiver and through it a path algebra, generates a set of relations as given by Schroll, Brauer Graph Algebras (arXiv:1612.00061v2), and creates an algebra by quotienting the path algebra by these relations.

The quiver is created in the following manner:

	(a) The vertices of the quiver are the edges of the Brauer Graph.
	(b) The edges (directed) of the quiver come from adjacency of edges in the Orientations.

So, for each vertex of the graph which is not a leaf, there is an associated cycle of quiver edges.

The relations are of three types:

	(i) Type 1: C1^m(v) - C2^m(v') = 0 where C1 is a cycle of the quiver associated to vertex v of the graph, C2 is a cycle of the quiver associated to vertex v' of the graph, and m is the funtion from the set of vertices to their multiplicities. The constraints are that there must be an edge joining v and v' on the graph (they could be the same vertex if there is a self loop), and the two cycles must start at the corresponding vertex of the quiver to that edge from the graph.
	(ii) Type 2: Each edge of the quiver is a member of a cycle. Given an edge e, we have the relation C^m(v)e = 0 where v is the vertex associated to C.
	(iii) Type 3: ab = 0 where a and b are edges of the quiver, the head of a is the tail of b, and ab is not a member of a cycle associated with a vertex from the Brauer Graph.

This results in a finite dimensional symmetric algebra (proof in Schroll).