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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

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