Deformations of chiral algebras

Details Deformations of chiral algebras Deformations of chiral algebras

2003-04-15

arxiv.org/abs/math/0304211v1

Proceedings of the ICM, Beijing 2002, vol. 2, 105--118

Mathematics

Quantum Algebra

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Deformations of chiral algebras does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Deformations of chiral algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Deformations of chiral algebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-608501