Application of a "Jacobi identity" for vertex operator algebras to zeta values and differential operators

TL;DR

This paper introduces a new Jacobi identity for vertex operator algebras and demonstrates its application in interpreting and extending work connecting zeta values at negative integers with a Lie algebra of operators.

Contribution

It presents a novel Jacobi identity for vertex operator algebras and applies it to generalize and interpret existing results relating zeta values and Lie algebras.

Findings

New Jacobi identity for vertex operator algebras

Generalization of Bloch's work on zeta values

Interpretation of zeta values via Lie algebra of operators

Abstract

We explain how to use a certain new "Jacobi identity" for vertex operator algebras, announced in a previous paper (math.QA/9909178), to interpret and generalize recent work of S. Bloch's relating values of the Riemann zeta function at negative integers with a certain Lie algebra of operators.