We describe the Hall algebra of an elliptic curve defined over a finite field and show that the group of exact autoequivalences of the derived category acts on the Drinfeld double of by algebra automorphisms. We study a certain natural subalgebra of for which we give a presentation by generators and relations. This algebra turns out to be a flat two-parameter deformation of the ring of diagonal invariants , that is, the ring of symmetric Laurent polynomials in two sets of countably many variables under the simultaneous symmetric group action.
"On the Hall algebra of an elliptic curve, I." Duke Math. J. 161 (7) 1171 - 1231, 15 May 2012. https://doi.org/10.1215/00127094-1593263