Symmetric Invariant Bilinear Forms on Modular Vertex Algebras

2017/11/03 by Li, Haisheng, Mu, Qiang
#17B68 #17B69 #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1711.00986

Abstract

In this paper, we study contragredient duals and invariant bilinear forms for modular vertex algebras (in characteristic p). We first introduce a bialgebra H and we then introduce a notion of H-module vertex algebra and a notion of (V,H)-module for an H-module vertex algebra V. Then we give a modular version of Frenkel-Huang-Lepowsky's theory and study invariant bilinear forms on an H-module vertex algebra. As the main results, we obtain an explicit description of the space of invariant bilinear forms on a general H-module vertex algebra, and we apply our results to affine vertex algebras and Virasoro vertex algebras.

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