Related papers: Modules over axial algebras
Axial algebras are a class of commutative non-associative algebras which have a natural group of automorphisms, called the Miyamoto group. The motivating example is the Griess algebra which has the Monster sporadic simple group as its…
An axial algebra is a commutative non-associative algebra generated by axes, that is, primitive, semisimple idempotents whose eigenvectors multiply according to a certain fusion law. The Griess algebra, whose automorphism group is the…
We introduce decomposition algebras as a natural generalization of axial algebras, Majorana algebras and the Griess algebra. They remedy three limitations of axial algebras: (1) They separate fusion laws from specific values in a field,…
Axial algebras are a class of commutative algebras generated by idempotents, with adjoint action semisimple and satisfying a prescribed fusion law. Axial algebras were introduced by Hall, Rehren, and Shpectorov in 2015 as a broad…
Axial algebras of Monster type are a class of non-associative algebras which generalise the Griess algebra, whose automorphism group is the largest sporadic simple group, the Monster. The $2$-generated algebras, which are the building…
Axial algebras are a class of commutative non-associative algebras generated by idempotents, called axes, with adjoint action semi-simple and satisfying a prescribed fusion law. Axial algebras were introduced by Hall, Rehren and Shpectorov…
Axial algebras of Monster type are a class of commutative algebras generated by special idempotents called axes. Some motivating examples of these algebras are the Griess algebra and the Norton-Sakuma algebras, relating to the Monster…
We extend the theory of Matsuo algebras, which are certain non-associative algebras related to 3-transposition groups, to characteristic 2. Instead of idempotent elements associated to points in the corresponding Fischer space, our algebras…
In the first half of this paper, we define axial algebras: nonassociative commutative algebras generated by axes, that is, semisimple idempotents---the prototypical example of which is Griess' algebra [C85] for the Monster group. When…
We review 3-transposition groups arising in vertex operator algebra theory. One can construct a commutative algebra called the Matsuo algebra out of a 3-transposition group. Some 3-transposition groups arise as automorphism groups of vertex…
Matsuo algebras are an algebraic incarnation of 3-transposition groups with a parameter $\alpha$, where idempotents takes the role of the transpositions. We show that a large class of idempotents in Matsuo algebras satisfy the Seress…
Axial algebras are a recently introduced class of non-associative algebra, with a naturally associated group, which generalise the Griess algebra and some key features of the moonshine VOA. Sakuma's Theorem classifies the eight…
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 of automorphisms and thus axial algebras…
An axial algebra $A$ is a commutative non-associative algebra generated by primitive idempotents, called axes, whose adjoint action on $A$ is semisimple and multiplication of eigenvectors is controlled by a certain fusion law. Different…
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 Conway-Miyamoto correspondences between…
Axial algebras are commutative algebras generated by idempotents; they generalise associative algebras by allowing the idempotents to have additional eigenvectors, controlled by fusion rules. If the fusion rules are $\mathbb{Z}/2$-graded,…
Majorana theory was introduced by A. A. Ivanov as the axiomatization of certain properties of the 2A-axes of the Griess algebra. Since its inception, Majorana theory has proved to be a remarkable tool with which to study objects related to…
In this paper, we determine the connected component of the automorphism group scheme of Matsuo algebras over fields of characteristic not $3$.
Axial algebras are non-associative algebras generated by semisimple idempotents, known as axes, that all obey a fusion rule. Axial algebras were introduced by Hall, Rehren and Shpectorov as a generalisation of the axioms of Majorana theory,…
We study the class of idempotent-generated pseudo-composition algebras, which is a subclass of the family of axial algebras. More specifically, we utilise the group-algebra correspondence, natural to the axial framework in order to study…