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arXiv · 2008.13178

Invariant Hermitian forms on vertex algebras

Victor G. Kac·Pierluigi Möseneder Frajria·Paolo Papi
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Abstract

We study invariant Hermitian forms on a conformal vertex algebra and on their (twisted) modules. We establish existence of a non-zero invariant Hermitian form on an arbitrary $W$-algebra. We show that for a minimal simple $W$-algebra $W_k(\mathfrak g,\theta/2)$ this form can be unitary only when its $\tfrac{1}{2}\mathbb Z$-grading is compatible with parity, unless $W_k(\mathfrak g,\theta/2)$ "collapses" to its affine subalgebra.

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BibTeXRIS

Victor G. Kac, Pierluigi Möseneder Frajria, Paolo Papi. 2020-08-30. Invariant Hermitian forms on vertex algebras. https://arxiv.org/abs/2008.13178

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