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 Wk(,/2) this form can be unitary only when its 1/2ℤ-grading is compatible with parity, unless Wk(#x1d524#x1d703/2) to its affine subalgebra.

Invariant Hermitian forms on vertex algebras

Pierluigi Moseneder Frajria;
2022-01-01

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 Wk(,/2) this form can be unitary only when its 1/2ℤ-grading is compatible with parity, unless Wk(#x1d524#x1d703/2) to its affine subalgebra.
2022
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1188415
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