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Pure Mathematics 2026
6A型顶点算子代数中一种平凡Miyamoto对合自同构
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Abstract:
本文针对6A型顶点算子代数中的Miyamoto对合自同构和自同构群的生成元做了研究。通过顶点算子代数中的一个Ising向量定义出的Miyamoto对合自同构，其在顶点算子代数与群论之间建立了重要联系。在顶点算子代数中，一般的Ising的对合自同构是非平凡的。在本文我们在6A型顶点算子代数中通过某个Ising向量构造出一种平凡的Miyamoto对合自同构，并且给出了6A型顶点算子代数的自同构群的所有生成元。
This paper investigates the Miyamoto involution and the generators of the automorphism group of the 6A vertex operator algebra. The Miyamoto involutions defined by Ising vectors and establish an important connection between vertex operator algebras and group theory. In vertex operator algebras, general Ising involutions are nontrivial. In this paper, we construct a trivial Miyamoto involution in the 6A vertex operator algebra, and we present all generators of the automorphism group of the 6A vertex operator algebra.
| [1] | Sakuma, S. and Yamauchi, H. (2003) Vertex Operator Algebra with Two Miyamoto Involutions Generating S3. Journal of Algebra, 267, 272-297. https://doi.org/10.1016/s0021-8693(03)00170-4 |
| [2] | Hung, L.C., Hiromichi, Y. and Hiroshi, Y. (2005) Mckay’s Observation and Vertex Operator Algebras Generated by Two Conformal Vectors of Central Charge 1/2. International Mathematics Research Papers, 3, 117-181. |
| [3] | Wang, W.Q. (1993) Rationality of Virasoro Vertex Operator Algebras. International Mathematics Research Notices, 7, 197-211. |
| [4] | Sakuma, S. (2007) 6-Transposition Property of-Involutions of Vertex Operator Algebras. International Mathematics Research Notices, 9, rnm030. |
| [5] | Miyamoto, M. (1996) Griess Algebras and Conformal Vectors in Vertex Operator Algebras. Journal of Algebra, 179, 523-548. https://doi.org/10.1006/jabr.1996.0023 |
| [6] | 武文斌. 6A型顶点算子代数中的Ising向量[J]. 理论数学, 2022, 12(10): 8. |
| [7] | Jiao, X. and Zheng, W. (2022) Vertex Operator Algebras Generated by Two Ising Vectors. Journal of Algebra, 610, 546-570. https://doi.org/10.1016/j.jalgebra.2022.07.034 |
