6-Transposition Property of τ-Involutions of Vertex Operator Algebras

By Shinya Sakuma. 2006

94 citations recorded by the source corpus.

In this paper, we study the subalgebra generated by two Ising vectors in the Griess algebra of a vertex operator algebra. We show that the structure of it is uniquely determined by some inner products of Ising vectors. We prove that the order of the product of two $\tau$-involutions is less than or equal to 6 and we determine the inner product of two Ising vectors.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2ff19a0b8dbe6fa7bc29addffc616f46ddbb682a

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In Algebra and Number Theory

1. J. Duncan
2. Sergey V. Shpectorov
3. Miranda C. N. Cheng
4. Jonathan I. Hall
5. J. Harvey
6. Yoav Segev

In Geometry and Topology

1. J. Duncan
2. Sergey V. Shpectorov
3. Miranda C. N. Cheng
4. Jonathan I. Hall
5. J. Harvey
6. Yoav Segev

In Mathematical Physics

1. J. Duncan
2. Sergey V. Shpectorov
3. Miranda C. N. Cheng
4. Jonathan I. Hall
5. J. Harvey
6. Yoav Segev

Citations in the corpus

• Primitive axial algebras of Jordan type (2014, methodology): “e groups that can be generated by these Miyamoto involutions within the automorphism groups of Griess algebras and their associated VOAs. Of particular importance for this paper is the work of Sakuma [Sa07], which described all groups generated by two such involutions, and that of Matsuo [Ma05], whi”
• Umbral Moonshine (2012, methodology): “We conclude by mentioning that McKay’s monstrous observation has partially been ex- plained, using vertex operator algebra theory, by the work of Sakuma [103] and Lam–Yamada– Yamauchi [104, 105].”