On the Hall algebra of an elliptic curve. I.
In this paper the authors give a description of the Hall algebra of an elliptic curve defined over a finite field and show that the group \(\mathrm{SL}(2,\mathbb Z)\) of exact autoequivalences of the bounded derived category of coherent sheaves on \(X\) acts on the Drinfeld double of the Hall algebra by algebra automorphisms. The authors also give a presentation, by generators and relations, of a subalgebra of the Hall algebra which is shown to coincide with Kapranov's spherical Hall algebra and of its Drinfeld double. The latter Drinfeld double is shown to be isomorphic to a flat two-parameter deformation of the ring of symmetric polynomials in two sets of countably many variables under the simultaneous action of the infinite symmetric group.
scientific article; zbMATH DE number 6047809
scientific article