Search

MiS Preprint Repository

Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.

MiS Preprint
28/2006

Full field algebras, operads and tensor categories

Liang Kong

Abstract

We study the operadic and categorical formulations of (conformal) full field algebras. In particular, we show that a grading-restricted R×R-graded full field algebra is equivalent to an algebra over a partial operad constructed from spheres with punctures and local coordinates. This result is generalized to conformal full field algebras over VL ⊗ VR, where VL and VR are two vertex operator algebras satisfying certain natural finite and reductive conditions. We also study the geometry interpretation of conformal full field algebras over VL ⊗ VR equipped with a nondegenerate invariant bi- linear form. By assuming slightly stronger conditions on VL and VR, we show that a conformal full field algebra over VL ⊗ VR equipped with a non- degenerate invariant bilinear form exactly corresponds to a commutative Frobenius algebra with a trivial twist in the category of VL ⊗ VR-modules. The so-called diagonal constructions [Y.-Z. Huang and L. Kong, Full field algebras, arXiv:math.QA/0511328.] of conformal full field algebras are given in tensor-categorical language.

Received:
Mar 15, 2006
Published:
Mar 15, 2006

Related publications

inJournal
2007 Repository Open Access
Liang Kong

Full field algebras, operads and tensor categories

In: Advances in mathematics, 213 (2007) 1, pp. 271-340