Abstract
Recent work in hypergraph Ramsey theory has involved the introduction of a "lifting map" that associates a certain 3-uniform hypergraph to a given graph, bounding cliques in a predictable way. In this paper, we interpret the lifting map as a linear transformation. This interpretation allows us to use algebraic techniques to prove several structural properties of the lifting map, culminating in new lower bounds for certain 3-uniform hypergraph Ramsey numbers.