• Corpus ID: 246035864

3-transposition groups arising in VOA theory

@inproceedings{Yamauchi20223transpositionGA,
  title={3-transposition groups arising in VOA theory},
  author={Hiroshi Yamauchi},
  year={2022}
}
We review 3-transposition groups arising in vertex operator algebra theory. One can construct a commutative algebra called the Matsuo algebra out of a 3transposition group. Some 3-transposition groups arise as automorphism groups of vertex operator algebras via Matsuo algebras but there exist some 3-transposition groups which do not arise through Matsuo algebras. We will exhibit examples of those groups together with VOAs. This article is based on the author’s talk at the seminar on “Majorana… 

References

SHOWING 1-10 OF 38 REFERENCES
3-transposition groups of symplectic type and vertex operator algebras
The 3-transposition groups that act on a vertex operator algebra in the way described by Miyamoto are classified under the assumption that the group is centerfree and the VOA carries a
The Conway-Miyamoto correspondences for the Fischer 3-transposition groups
In this paper, we present a general construction of 3-transposition groups as automorphism groups of vertex operator algebras. Applying to the moonshine vertex operator algebra, we establish the
6-Transposition Property of τ-Involutions of Vertex Operator Algebras
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
Griess Algebras and Conformal Vectors in Vertex Operator Algebras
Abstract We define automorphisms of vertex operator algebra using the representations of the Virasoro algebra. In particular, we show that the existence of a special element, which we will call a
AN EXPLICIT MAJORANA REPRESENTATION OF THE GROUP 3(2):2 OF 3C-PURE TYPE
In this article, we study Griess algebras and vertex operator subalgebras generated by Ising vectors in a moonshine type VOA such that the subgroup generated by the corresponding Miyamoto involutions
3-State Potts Model and Automorphisms of Vertex Operator Algebras of Order 3☆
Abstract We study the fusion rules of a vertex operator algebra W (0) +  R , which is a VOA over the real number field R and has a positive definite invariant bilinear form, and such that its
...
...