Integral forms in vertex operator algebras which are invariant under finite groups

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Integral forms in vertex operator algebras which are invariant under finite groups

For certain vertex operator algebras (e.g., lattice type) and given finite group of automorphisms, we prove existence of a positive definite integral form invariant under the group. Applications include an integral form in the Moonshine VOA which is invariant under the Monster, and examples in other lattice type VOAs.

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Compact automorphism groups of vertex operator algebras

Let V be a simple vertex operator algebra which admits the continuous, faithful action of a compact Lie group G of automorphisms. We establish a Schur-Weyl type duality between the unitary, irreducible modules for G and the irreducible modules for V G which are contained in V where V G is the space of G-invariants of V. We also prove a concomitant Galois correspondence between vertex operator s...

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Simple vertex operator algebras are nondegenerate

In this paper it is shown that every irreducible vertex algebra of countable dimension and every simple vertex operator algebra is nondegenerate in the sense of Etingof and Kazhdan.

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Rational vertex operator algebras are finitely generated

It is proved that any vertex operator algebra for which the image of the Virasoro element in Zhu’s algebra is algebraic over complex numbers is finitely generated. In particular, any vertex operator algebra with a finite dimensional Zhu’s algebra is finitely generated. As a result, any rational vertex operator algebra is finitely generated. Although many well known vertex operator algebras are ...

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Semi-infinite forms and topological vertex operator algebras

Semi-infinite forms on the moduli spaces of genus-zero Riemann surfaces with punctures and local coordinates are introduced. A partial operad for semi-infinite forms is constructed. Using semi-infinite forms and motivated by a partial suboperad of the partial operad for semi-infinite forms, topological vertex partial operads of type k < 0 and strong topological vertex partial operads of type k ...

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ژورنال

عنوان ژورنال: Journal of Algebra

سال: 2012

ISSN: 0021-8693

DOI: 10.1016/j.jalgebra.2012.05.006