The A-infinity algebra of an Elliptic Curve and the j-invariant

Robert Fisette

Published 2011-11-27Version 1

We compute reduced Hochschild cohomology of B = Ext\star (O \oplus L, O \oplus L), where O is the structure sheaf of an elliptic curve and L is a line bundle of degree 1. The result suggests an A-infinity equivalence between the A-infinity structure computed for B in [1] and a structure in which m_3=m_4=m_5=0. We see that the j-invariant of the curve is explicitly related to this new structure.