Semantic Scholar Open Access 2006 33 sitasi

Full field algebras, operads and tensor categories

Liang Kong

Lihat Sumber DOI

Abstrak

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 V L ⊗ V R , where V L and V R are two vertex operator algebras satisfying certain finiteness and reductivity conditions. We also study the geometry interpretation of conformal full field algebras over V L ⊗ V R equipped with a nondegenerate invariant bilinear form. By assuming slightly stronger conditions on V L and V R , we show that a conformal full field algebra over V L ⊗ V R equipped with a nondegenerate invariant bilinear form exactly corresponds to a commutative Frobenius algebra with a trivial twist in the category of V L ⊗ V R -modules. The so-called diagonal constructions [Y.-Z. Huang, L. Kong, Full field algebras, arXiv: math.QA/0511328 ] of conformal full field algebras are given in tensor-categorical language.

Topik & Kata Kunci

Mathematics Physics

Penulis (1)

Liang Kong

Format Sitasi

APA MLA BibTeX

Kong, L. (2006). Full field algebras, operads and tensor categories. https://doi.org/10.1016/j.aim.2006.12.007

Akses Cepat

Lihat di Sumber doi.org/10.1016/j.aim.2006.12.007

Informasi Jurnal

Tahun Terbit: 2006
Bahasa: en
Total Sitasi: 33×
Sumber Database: Semantic Scholar
DOI: 10.1016/j.aim.2006.12.007
Akses: Open Access ✓