Linear automorphisms of vertex operator algebras associated with formal changes of variable and Bernoulli-type numbers

2014/01/24 by Robert McRae, McRae, Robert
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #math.NT #math.QA #msc:17B69

paper · pdf · doi:10.48550/arxiv.1401.6442

14 pages, references added

arxiv created 2014/07/07 · arxiv updated 2014/07/08

Abstract

We study a certain linear automorphism of a vertex operator algebra induced by the formal change of variable f(x)=e^x-1 and describe examples showing how this relates the theory of vertex operator algebras to Bernoulli numbers, Bernoulli polynomial values, and related numbers. We give a recursion for such numbers derived using vertex operator relations, and study the Jacobi identity for modified vertex operators that was introduced in work of Lepowsky.

Related

• Introduction to vertex operator algebras II
• Twisted modules for vertex operator algebras and Bernoulli polynomials
• A classical vertex algebra constructed with the use of some logarithmic formal calculus
• Some developments in vertex operator algebra theory, old and new
• Vertex operator algebras and the zeta function