## 66 Citations

### Miyamoto involutions in axial algebras of Jordan type half

- Mathematics
- 2016

Nonassociative commutative algebras A, generated by idempotents e whose adjoint operators ade: A → A, given by x ↦ xe, are diagonalizable and have few eigenvalues, are of recent interest. When…

### Axial algebras of Jordan and Monster type

- Mathematics
- 2022

Axial algebras are a class of non-associative commutative algebras whose properties are deﬁned in terms of a fusion law. When this fusion law is graded, the algebra has a naturally associated group…

### Structure of primitive axial algebras

- Mathematics
- 2022

. “Fusion rules” are laws of multiplication among eigenspaces of an idempotent. This terminology is relatively new and is closely related to primitive axial algebras, introduced recently by Hall,…

### Axes of Jordan type in non-commutative algebras

- Mathematics
- 2021

The Peirce decomposition of a Jordan algebra with respect to an idempotent is well known. This decomposition was taken one step further and generalized recently by Hall, Rehren and Shpectorov, with…

### On the structure of axial algebras

- MathematicsTransactions of the American Mathematical Society
- 2019

Axial algebras are commutative non-associative algebras generated by axes, that is, idempotents satisfying a fixed fusion law. In this paper, we introduce a natural equivalence relation on sets of…

## References

SHOWING 1-10 OF 28 REFERENCES

### Griess Algebras and Conformal Vectors in Vertex Operator Algebras

- Mathematics
- 1996

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…

### Vertex algebras, Kac-Moody algebras, and the Monster.

- MathematicsProceedings of the National Academy of Sciences of the United States of America
- 1986

An integral form is constructed for the universal enveloping algebra of any Kac-Moody algebras that can be used to define Kac's groups over finite fields, some new irreducible integrable representations, and a sort of affinization of anyKac-moody algebra.

### Lie Algebras and Cotriangular Spaces

- Mathematics
- 2005

Let p (P,L) be a partial linear space in which any line contains three points and let K be a field. Then by LK(p) we denote the free K-algebra generated by the elements of P and subject to the…

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

- Mathematics
- 2006

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…

### 3-transposition groups of symplectic type and vertex operator algebras

- Mathematics
- 2003

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…

### A construction of F(1) as automorphisms of a 196,883-dimensional algebra.

- MathematicsProceedings of the National Academy of Sciences of the United States of America
- 1981

The construction of the finite simple group F(1), whose existence was predicted independently in 1973 by Bernd Fischer and by me is announced, and implies the existence of a number of other sporadic simple groups for which existence proofs formerly depended on work with computers.