Mathematical Research Letters

Volume 11 (2004)

Number 5

$K$-theory associated to vertex operator algebras

Pages: 629 – 647

DOI: http://dx.doi.org/10.4310/MRL.2004.v11.n5.a7

Authors

Chongying Dong (University of California at Santa Cruz)

Kefeng Liu (University of California at Los Angeles)

Xiaonan Ma (Ecole Polytechnique)

Jian Zhou (Qinghua University)

Abstract

We introduce two $K$-theories, one for vector bundles whose fibers are modules of vertex operator algebras, another for vector bundles whose fibers are modules of associative algebras. We verify the cohomological properties of these $K$-theories, and construct a natural homomorphism from the VOA $K$-theory to the associative algebra $K$-theory.

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