相关论文: An infinite-dimensional 2-generated primitive axia…
We provide the basic setup for the project, initiated by Felix Rehren, aiming at classifying all 2-generated axial algebras of Monster type $(\alpha,\beta)$ over a field $\mathbb F$. Using this, we first show that every such algebra has…
In this paper we prove that $2$-generated primitive axial algebras of Monster type $(2\beta, \beta)$ over a ring $R$ in which $2$ and $\beta$ are invertible can be generated as $R$-module by $8$ vectors. We then completely classify…
Recently Takahiro Yabe gave an almost complete classification of primitive symmetric $2$-generated axial algebras of Monster type. In this note, we construct a new infinite-dimensional primitive $2$-generated symmetric axial algebra of…
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 show that primitive 4-generated axial algebras of Jordan type are at most 81-dimensional.
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,…
In our first paper, we looked at $2$-generated primitive axial algebras of Monster type with skew axet $X'(1+2)$. We continue our work by focusing on larger skew axets and classifying all such algebras with skew axets. This brings us one…
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…
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 show that if $k$ is a countable field, then there exists a finitely generated, infinite-dimensional, primitive algebraic $k$-algebra $A$ whose Gelfand-Kirillov dimension is at most six. In addition to this we construct a two-generated…
We consider Majorana algebras generated by three Majorana axes $a_0$, $a_1$ and $a_2$ such that $a_0$ and $a_1$ generate a dihedral algebra of type 2A. We show that such an algebra must occur as a Majorana representation of one of 27…
A class of axial algebras generated by two axes with eigenvalues 0, 1, $\eta$ and $\xi$ called axial algebras of Majorana type is introduced and classified when they are 2-generated, over fields of characteristics neither 2 nor 5 and there…
Axial algebras are a class of non-associative algebra with a strong link to finite (especially simple) groups which have recently received much attention. Of primary interest are the axial algebras of Monster type $(\alpha, \beta)$, of…
In earlier work we studied the structure of primitive axial algebras of Jordan type (PAJ's), not necessarily commutative, in terms of their primitive axes. In this paper we weaken primitivity and permit several pairs of (left and right)…
Skew axets were first defined by McInroy and Shpectorov where they used the term of axets to classify shapes of an algebra. When they first submitted their paper, it was not known if skew axial algebras exist and now we will present such…
The conjugacy classes of the Monster which occur in the McKay observation correspond to the isomorphism types of certain 2-generated subalgebras of the Griess algebra. Sakuma, Ivanov and others showed that these subalgebras match the…
Axial algebras of Jordan type $\eta$ are commutative algebras generated by idempotents whose adjoint operators have the minimal polynomial dividing $(x-1)x(x-\eta)$, where $\eta\not\in\{0,1\}$ is fixed, with restrictive multiplication…
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…
The notion of axial algebra is closely related to $3$-transposition groups, the Monster group and vertex operator algebras. In this work we continue our previous works and compete the proof that all algebras generated by a set of primitive…
Motivated by Yabe's classification of symmetric $2$-generated axial algebras of Monster type, we introduce a large class of algebras of Monster type $(\alpha, \frac{1}{2})$, generalising Yabe's $\mathrm{III}(\alpha,\frac{1}{2}, \delta)$…