July, 2024 The irreducible weak modules for the fixed point subalgebra of the vertex algebra associated to a non-degenerate even lattice by an automorphism of order 2 (Part 2)
Kenichiro TANABE
Author Affiliations +
J. Math. Soc. Japan 76(3): 813-854 (July, 2024). DOI: 10.2969/jmsj/89848984

Abstract

Let $V_{L}$ be the vertex algebra associated to a non-degenerate even lattice $L$, $\theta$ the automorphism of $V_{L}$ induced from the $-1$ symmetry of $L$, and $V_{L}^{+}$ the fixed point subalgebra of $V_{L}$ under the action of $\theta$. In this series of papers, we classify the irreducible weak $V_{L}^{+}$-modules and show that any irreducible weak $V_{L}^{+}$-module is isomorphic to a weak submodule of some irreducible weak $V_{L}$-module or to a submodule of some irreducible $\theta$-twisted $V_{L}$-module. Let $M(1)^{+}$ be the fixed point subalgebra of the Heisenberg vertex operator algebra $M(1)$ under the action of $\theta$. In this paper (Part 2), we show that there exists an irreducible $M(1)^{+}$-submodule in any non-zero weak $V_{L}^{+}$-module and we compute extension groups for $M(1)^{+}$.

Funding Statement

This research was partially supported by the Grant-in-aid (No. 21K03172) for Scientific Research, JSPS.

Citation

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Kenichiro TANABE. "The irreducible weak modules for the fixed point subalgebra of the vertex algebra associated to a non-degenerate even lattice by an automorphism of order 2 (Part 2)." J. Math. Soc. Japan 76 (3) 813 - 854, July, 2024. https://doi.org/10.2969/jmsj/89848984

Information

Received: 1 July 2022; Revised: 30 December 2022; Published: July, 2024
First available in Project Euclid: 6 August 2023

Digital Object Identifier: 10.2969/jmsj/89848984

Subjects:
Primary: 17B69

Keywords: lattices , vertex algebras , weak modules

Rights: Copyright ©2024 Mathematical Society of Japan

Vol.76 • No. 3 • July, 2024
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