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15 May 2012 On the Hall algebra of an elliptic curve, I
Igor Burban, Olivier Schiffmann
Duke Math. J. 161(7): 1171-1231 (15 May 2012). DOI: 10.1215/00127094-1593263

Abstract

We describe the Hall algebra HX of an elliptic curve X defined over a finite field and show that the group SL(2,Z) of exact autoequivalences of the derived category Db(Coh(X)) acts on the Drinfeld double DHX of HX by algebra automorphisms. We study a certain natural subalgebra UX of DHX 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 C[x1±1,,y1±1,]S, that is, the ring of symmetric Laurent polynomials in two sets of countably many variables under the simultaneous symmetric group action.

Citation

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Igor Burban. Olivier Schiffmann. "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

Information

Published: 15 May 2012
First available in Project Euclid: 4 May 2012

zbMATH: 1286.16029
MathSciNet: MR2922373
Digital Object Identifier: 10.1215/00127094-1593263

Subjects:
Primary: 16T05
Secondary: 22E65

Rights: Copyright © 2012 Duke University Press

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Vol.161 • No. 7 • 15 May 2012
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