相关论文: Constructing Majorana Representations

Graph transformation is concerned with the manipulation of graphs by means of rules. Graph grammars have been traditionally studied using techniques from category theory. In previous works, we introduced Matrix Graph Grammars (MGGs) as a…

The goal of this paper is to consider some relations between varieties of representations of groups and varieties of associative algebras. The main emphasis is put on the varieties of representations of groups induced by the varieties of…

The notion of Poisson dialgebras was introduced by Loday. In this article, we propose a new definition with some modifications that is supported by several canonical examples coming from Poisson algebra modules, averaging operators on…

We construct a self-dual integral form of the moonshine vertex operator algebra, and show that it has symmetries given by the Fischer-Griess monster simple group. The existence of this form resolves the last remaining open assumption in the…

The construction of algebraic structure of central molecular chirality is provided starting from the empirical Fischer projections for tetrahedrons. A matrix representation is given and the algebra of O(4) orthogonal group for rotations and…

A monoid structure on families of representations of a quiver is introduced by taking extensions of representations in families, i.e. subvarieties of the varieties of representations. The study of this monoid leads to interesting…

By the classical genus zero Sugawara construction one obtains from admissible representations of affine Lie algebras (Kac-Moody algebras of affine type) representations of the Virasoro algebra. In this lecture first the classical…

Iwasawa algebras of compact $p$-adic Lie groups are completed group algebras with applications in number theory in studying class numbers of towers of number fields and representation theory of $p$-adic Lie groups. In our earlier work, we…

In the late 1980s, Friedlander and Parshall studied the representations of a family of algebras which were obtained as deformations of the distribution algebra of the first Frobenius kernel of an algebraic group. The representation theory…

Majorana fermions are the real (in a mathematical sense) counterparts of complex fermions like ordinary electrons. The promise of topological quantum computing has lead to substantial experimental progress in realizing these particles in…

We discuss how basic Clifford algebra and indeed all of matrix algebra and matrix representations of finite groups comes from Iterants: very elementary processes such as an alternation of plus and minus one ...+-+-+- .... One can think of…

Theory of representations of universal algebra is a natural development of the theory of universal algebra. Morphism of the representation is the map that conserve the structure of the representation. Exploring of morphisms of the…

A new class of integrable mappings and chains is introduced. Corresponding $(1+2)$ integrable systems invariant with respect to such discrete transformations are presented in an explicit form. Their soliton-type solutions are constructed in…

In this article we give an elementary introduction to the representation theory of finite magnetic groups from a purely mathematical point of view. -- En este art\'iculo damos una introducci\'on elemental a la teor\'ia de representaciones…

It is shown how to obtain recently-proposed two-zero Majorana mass textures in models with three Higgs triplets with small VEVs and a sufficiently massive triplet Majoron by using abelian discrete symmetries. It is briefly discussed how in…

Majorana's arbitrary spin theory is considered in a hyperbolic complex representation. The underlying differential equation is embedded into the gauge field theories of Sachs and Carmeli. In particular, the approach of Sachs can serve as a…

This paper is dedicated to the memory of Zbigniew Oziewicz, to his generosity, intelligence and intensity in the search that is science and mathematics. The paper begins with a basic construction that produces Clifford algebras inductively,…

The primary purpose is to introduce and explore projective varieties, $\text{GRASS}_{\bf d}(\Lambda)$, parametrizing the full collection of those modules over a finite dimensional algebra $\Lambda$ which have dimension vector $\bf d$. These…

The simplest possibility to generate small Majorana neutrino masses is the seesaw mechanism. However, the smallness of the observed neutrino masses can also be understood, if neutrino masses are generated by higher-dimensional operators…

In the 1980's, the work of Frenkel, Lepowsky and Meurman, along with that of Borcherds, culminated in the notion of vertex operator algebra, and an example whose full symmetry group is the largest sporadic simple group: the Monster. Thus it…