In this paper, we construct two spanning sets for the affine algebraic curvature tensors. We then prove that every 2-dimensional affine algebraic curvature tensor can be represented by a single element from either of the two spanning sets. This paper provides a means to study affine algebraic curvature tensors in a geometric and algebraic manner similar to previous studies of canonical algebraic curvature tensors.
Kelly, Stephen J.
"Constructing Spanning Sets of Affine Algebraic Curvature Tensors,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 24:
1, Article 5.
Available at: https://scholar.rose-hulman.edu/rhumj/vol24/iss1/5