相关论文: Automorphism Properties of Adinkras
The problem of classifying off-shell representations of the $N$ -extended one-dimensional super Poincar\'e algebra is closely related to the study of a class of decorated $N$-regular, $N$-edge colored bipartite graphs known as Adinkras. In…
Adinkras are graphs that can describe off-shell supermultiplets in 1 dimension with a Lie superalgebra known as Garden algebra. In this paper, I show that the degrees of freedom of the adinkra can be represented by a subgraph called a…
We classify the automorphic representations (over number fields) and the irreducible admissible representations (over local fields) of unitary groups which are not quasi-split, under the assumption that the same is known for quasi-split…
We are interested in overgroups of the automorphism group of the Rado graph. One class of such overgroups is completely understood; this is the class of reducts. In this article we tie recent work on various other natural overgroups, in…
By a map we mean a $2$-cell decomposition of a closed compact surface, i.e., an embedding of a graph such that every face is homeomorphic to an open disc. Automorphism of a map can be thought of as a permutation of the vertices which…
The aim of this work is to offer a solution to the problem of the classification of endomorphisms with an annihilating polynomial on arbitrary vector spaces. For these endomorphisms we provide a family of invariants that allows us to…
Artificial intelligence (AI) has emerged as a transformative influence, engendering paradigm shifts in global societies, spanning academia and industry. However, in light of these rapid advances, addressing the underrepresentation of black…
In this article, we characterize the (covariant) isotropy groups of free, finitely generated racks and quandles. As a consequence, we show that the usual inner automorphisms of such racks and quandles are precisely those automorphisms that…
We study the automorphism group of an idempotent evolution algebra, show that any finite group can be the automorphism group of an evolution algebra, and describe certain evolution algebras with given automorphism groups. In particular, we…
We initiate the study of analogues of symmetric spaces for the family of finite dihedral groups. In particular, we investigate the structure of the automorphism group, characterize the involutions of the automorphism group, and determine…
We explain how the redefinitions of supermultiplet component fields, comprising what we call "frame shifts", can be used in conjuction with the graphical technology of multiplet Adkinras to render manifest the reducibility of off-shell…
Recent efforts to classify representations of supersymmetry with no central charge have focused on supermultiplets that are aptly depicted by Adinkras, wherein every supersymmetry generator transforms each component field into precisely one…
Motivated by the search for embedded on-shell supermultiplets in higher dimensional off-shell theories, we investigate several 16-color supermultiplets and their topology. An Adinkra's topology is known to be equivalent to…
This paper focuses on the derivations and automorphism groups of certain finite-dimensional associative algebras over the field of complex numbers. Using classification results for algebras of dimensions two, three, and four, along with…
We prove that the automorphism group of the dihedral quandle with n elements is isomorphic to the affine group of the integers mod n, and also obtain the inner automorphism group of this quandle. In [9], automorphism groups of quandles (up…
The principal filtration of the infinite-dimensional odd Contact Lie superalgebra over a field of characteristic $p>2$ is proved to be invariant under the automorphism group by investigating ad-nilpotent elements and determining certain…
The problem of classifying off-shell representations of the $N$-extended one-dimensional super Poincar\'{e} algebra is closely related to the study of a class of decorated $N$-regular, $N$-edge colored bipartite graphs known as {\em…
Adinkra networks arise in the Carroll limit of supersymmetric QFT. Extensions of adinkras that are infinite dimensional graphs have never previously been discussed in the literature. We call these "infinite unfolded'' adinkras and study the…
We classify isomorphism-invariant random digraphs according to where randomness resides, namely, arcs, vertices, and vertices and arcs together which in turn yield arc random digraphs (ARD), vertex random digraphs (VRD) and vertex-arc…
"Pure" homogeneous linear supermultiplets (minimal and non-minimal) of the N=4-Extended one-dimensional Supersymmetry Algebra are classified. "Pure" means that they admit at least one graphical presentation (the corresponding graph/graphs…