Monomials, graphs and determinants

Such algebras possess projector bases, which, in important examples involving group algebras, are used in the construction of gauge-invariant operators. The centres of group algebras also possess bases labelled by conjugacy classes, and small subsets of these basis elements can form non-linear generating sets.

We propose a new linear basis for a CASS algebra, constructed from monomials in an ordered set of the generators. We describe how the relevant algebra data is encoded in a layered degeneracy graph, whose combinatorial structure determines the proposed monomials. We discuss how the number of these monomials matches the dimension of the algebra. Lastly, we discuss the matrix relating the proposed monomials to the projector basis and conjecture a general non-vanishing formula for its determinant.