$C_2$-Cofiniteness and Rationality of the Icosahedral Orbifold $V_{L_2}^{A_5}$

Abstract

Let $L_2=\mathbb{Z}α$ be the rank-one root lattice with $(α,α)=2$, and let $A_5$ act on the lattice vertex operator algebra $V_{L_2}$ through an icosahedral subgroup of $\operatorname{Aut}(V_{L_2})\cong PSL_2(\mathbb{C})$. We prove that the fixed-point vertex operator algebra $V_{L_2}^{A_5}$ is $C_2$-cofinite and strongly rational.

Disclosure

“thesis-independent audit of the explicit irreducible-module list, as well as intrinsic characterization of VLA25 , remains separate work. Acknowledgments We gratefully acknowledge the use of OpenAI’s GPT5.6 Sol model as a research assistance tool in the preparation of this manuscript. The model was employed to support literature ex- ploration, conceptual brainstorming, and language polishing, which contributed to improving the clarity and effi”

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Classification

Brainstorming or outlining

Multiplier

2

Verified

2026-08-23T05:15:06.241897Z

Structural counts