Duke Mathematical Journal
- Duke Math. J.
- Volume 161, Number 7 (2012), 1171-1231.
On the Hall algebra of an elliptic curve, I
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.
Duke Math. J., Volume 161, Number 7 (2012), 1171-1231.
First available in Project Euclid: 4 May 2012
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 16T05: Hopf algebras and their applications [See also 16S40, 57T05]
Secondary: 22E65: Infinite-dimensional Lie groups and their Lie algebras: general properties [See also 17B65, 58B25, 58H05]
Burban, Igor; Schiffmann, Olivier. On the Hall algebra of an elliptic curve, I. Duke Math. J. 161 (2012), no. 7, 1171--1231. doi:10.1215/00127094-1593263. https://projecteuclid.org/euclid.dmj/1336142074