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 (,/2) this form can be unitary only when its 1/2ℤ-grading is compatible with parity, unless (,/2) “collapses” to its affine subalgebra.
Invariant Hermitian forms on vertex algebras / Kac, Victor G.; Möseneder Frajria, Pierluigi; Papi, Paolo. - In: COMMUNICATIONS IN CONTEMPORARY MATHEMATICS. - ISSN 0219-1997. - (2022). [10.1142/S0219199721500590]
Invariant Hermitian forms on vertex algebras
Paolo Papi
2022
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 (,/2) this form can be unitary only when its 1/2ℤ-grading is compatible with parity, unless (,/2) “collapses” to its affine subalgebra.File allegati a questo prodotto
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