Primitive axial algebras of Jordan type

  title={Primitive axial algebras of Jordan type},
  author={J. I. Hall and Felix Rehren and Sergey V. Shpectorov},
  journal={Journal of Algebra},

Miyamoto involutions in axial algebras of Jordan type half

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

An expansion algorithm for constructing axial algebras

Axial algebras of Jordan and Monster type

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

Enumerating 3-generated axial algebras of Monster type

Split spin factor algebras

Universal axial algebras and a theorem of Sakuma

Structure of primitive axial algebras

. “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

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

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



Universal axial algebras and a theorem of Sakuma

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

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

  • R. Borcherds
  • Mathematics
    Proceedings 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

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

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

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.

  • R. Griess
  • Mathematics
    Proceedings 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.