相关论文: Minimal 3-generated Majorana algebras
A class of axial decomposition algebras with Miyamoto group generated by two Miyamoto automorphisms and three eigenvalues $0,1$ and $\eta$ is introduced and classified in the case with $\eta\notin\{0,1,\frac{1}{2}\}$. This class includes…
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…
Over a field of characteristic 0, the algebra of invariants of several $n\times n$ matrices under simultameous conjugation by $GL_n$ is generated by traces of products of generic matrices. Teranishi, 1986, found a minimal system of eleven…
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…
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…
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…
The least upper bound on degrees of elements of a minimal system of generators of the algebra of invariants of 3x3 matrices is found, and the nilpotency degree of a relatively free finitely generated algebra with the identity x^3=0 is…
An axial algebra over the field $\mathbb F$ is a commutative algebra generated by idempotents whose adjoint action has multiplicity-free minimal polynomial. For semisimple associative algebras this leads to sums of copies of $\mathbb F$.…
We introduce the Z_2-extended Griess algebra of a vertex operator superalgebra with an involution and derive the Matsuo-Norton trace formulae for the extended Griess algebra based on conformal design structure. We illustrate an application…
We consider a series of VOAs generated by 3-dimensional Griess algebras. We will show that these VOAs can be characterized by their 3-dimensional Griess algebras and their structures are uniquely determined. As an application, we will…
We calculate the spectrum of the diagram for each finite $3$-transposition group. Such graphs with a given minimal eigenvalue have occurred in the context of compact Griess subalgebras of vertex operator algebras.
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…
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…
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…
In this paper we study unitary braid group representations associated with Majorana Fermions. Majorana Fermions are represented by Majorana operators, elements of a Clifford algebra. The paper recalls and proves a general result about braid…
The Pimenov algebra with two generators is defined and some of its properties are shown. Some exact matrix over the Pimenov algebra representations of the motions group of Galilean plane (the Galilean group) are considered. A geometric…
We find a minimal set of generators for the coordinate ring of Calogero-Moser space $\mathcal{C}_3$ and the algebraic relations among them explicitly. We give a new presentation for the algebra of $3\times3$ invariant matrices involving the…
Indexed monoidal algebras are introduced as an equivalent structure for self-dual compact closed categories, and a coherence theorem is proved for the category of such algebras. Turing automata and Turing graph machines are defined by…
It is a classical problem to compute a minimal set of invariant polynomial generating the invariant ring of a finite group as an algebra. We present here an algorithm for the computation of minimal generating sets in the non-modular case.…
This is an improved version of the talk of the author given at the Antalya Algebra Days VII on May 21, 2005. We present an introduction to the theory of the invariants under the action of GL(n,C) by simultaneous conjugation of d matrices of…