Norton's Trace Formulae for the Griess Algebra¶of a Vertex Operator Algebra with Larger Symmetry

By A. Matsuo. 2000

49 citations recorded by the source corpus.

Abstract: Formulae expressing the trace of the composition of several (up to five) adjoint actions of elements of the Griess algebra of a vertex operator algebra are derived under certain assumptions on the action of the automorphism group. They coincide, when applied to the moonshine module V, with the trace formulae obtained in a different way by S. Norton, and the spectrum of some idempotents related to 2A, 2B, 3A and 4A elements of the Monster is determined by the representation theory of the Virasoro algebra at c= 1/2, the W3 algebra at c= 4/5 or the W4 algebra at c= 1. The generalization to the trace function on the whole space is also given for the composition of two adjoint actions, which can be used to compute the McKay-Thompson series for a 2A involution of the Monster.

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/b48a5fe534af3a6d8c503ee619d7c974c96aed1a

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In Algebra and Number Theory

1. C. Lam
2. Gerald Hoehn
3. Kazuya Kawasetsu
4. C. Dong

In Geometry and Topology

1. C. Lam
2. Gerald Hoehn
3. Kazuya Kawasetsu
4. C. Dong

In Statistical and Nonlinear Physics

1. Gerald Hoehn
2. Kazuya Kawasetsu
3. C. Lam
4. C. Dong

Citations in the corpus

• The Intermediate Vertex Subalgebras of the Lattice Vertex Operator Algebras (2013, result): “he subalgebra and module form a basis of the solutions of the modular differential equation (1) with µ= 551/900. Note that by means of Tuite’s result in [33], which was motivated by the work of Matsuo [25], our result can be thought of as a conformal field theory version of filling in the “hole” of the”
• W -algebras related to parafermion algebras (2008, background): “W -ALGEBRAS RELATED TO PARAFERMION ALGEBRAS 3 Section 3, Appendix B], [ 21, Section 4 ]).”
• Conformal designs based on vertex operator algebras (2007, methodology): “If V2 is a conformal 7-design, one obtains however d0 = 441768 37 which is impossible (cf. [ Mat01 ], Table 3.3).”