2003/04/15 by Dimitri Tamarkin
Mathematics · #math.QA #msc:14 #msc:18
published as Proceedings of the ICM, Beijing 2002, vol. 2, 105--118
arxiv created 2003/04/15 · arxiv updated 2009/11/30
We start studying chiral algebras (as defined by A. Beilinson and V. Drinfeld) from the point of view of deformation theory. First, we define the notion of deformation of a chiral algebra on a smooth curve X over a bundle of local artinian commutative algebras on X equipped with a flat connection (whereas `usual' algebraic structures are deformed over a local artinian algebra) and we show that such deformations are controlled by a certain *-Lie algebra \mathfrak g. Then we try to contemplate a possible additional structure on \mathfrak g and we conjecture that this structure up to homotopy is a chiral analogue of Gerstenhaber algebra, i.e. a coisson algebra with odd coisson bracket (in the terminology of Beilinson-Drinfeld). Finally, we discuss possible applications of this structure to the problem of quantization of coisson algebras.