相关论文: Automorphism Properties of Adinkras

In this note, firstly we give an easy proof of the factorization of symmetric matrices (see [Mos] math-ph/0203023), then we use it to prove the well-known fact that the automorphism group of a non-degenerate symmetric bilinear form acts…

In practice symmetries of combinatorial structures are computed by transforming the structure into an annotated graph whose automorphisms correspond exactly to the desired symmetries. An automorphism solver is then employed to compute the…

We consider differential rings of the form (K[x; y];D), where K is an algebraically closed field of characteristic zero and D : K[x; y] \to K[x; y] is a K-derivation. We study the Automorphism Group of such a ring and give criteria for…

The CREAM GAP package computes automorphisms, congruences, endomorphisms and subalgebras of algebras with an arbitrary number of binary and unary operations; it also decides if between two such algebras there exists a monomorphism, an…

We discuss the mechanism by which adinkras holographically store the required information for the Spin(1,3) Clifford Algebra fiber bundle in the cases of three 4D, N=1 representations: the chiral, vector and tensor supermultiplets.

In this work, we establish a relationship between the sum of irreducible character degrees and the number of twisted involutions associated with the automorphisms of a finite group. We develop algorithmic frameworks for evaluating these…

The regular objects in various categories, such as maps, hypermaps or covering spaces, can be identified with the normal subgroups N of a given group \Gamma, with quotient group isomorphic to \Gamma/N. It is shown how to enumerate such…

In this article, we consider involutions, called togglings, on the set of independent sets of the Dynkin diagram of type A, or a path graph. We are interested in the action of the subgroup of the symmetric group of the set of independent…

We introduce a group naturally acting on aperiodic necklaces of length $n$ with two colours using the 1--1 correspondences between aperiodic necklaces and irreducible polynomials over the field $\F_2$ of two elements. We notice that this…

A detailed proof is given of a theorem describing the centraliser of a transitive permutation group, with applications to automorphism groups of objects in various categories of maps, hypermaps, dessins, polytopes and covering spaces, where…

Using adjoint representation of Lie algebras, we calculate the automorphism group and ad-invariant metric on six dimensional solvable real Lie algebras with 5, 4 and 3 dimensional nilradicals.

Primarily this paper presents an expository report on alternatives to the traditional methods of classifying representations of finite dimensional algebras. Some new results illustrating such alternatives for algebras with only finitely…

Let Lambda be a tiled R-order. We give a description of Aut_R(Lambda) as the semidirect product of Inn(Lambda) and a certain subgroup of Aut(Q(Lambda)), where Q(Lambda) is the link graph of Lambda. Additionally, we give criteria for…

We produce a long exact sequence whose terms are unit groups of associative algebras that behave as inner automorphisms of a given tensor. Our sequence generalizes known sequences for associative and non-associative algebras. In a manner…

We show that the automorphism group of the complex of pants decompositions for a surface is isomorphic to the mapping class group for that surface.

The automorphism group of a curve is studied from the viewpoint of the canonical embedding and Petri's theorem. A criterion for identifying the automorphism group as an algebraic subgroup the general linear group is given. Furthermore the…

Autoencoders are techniques for data representation learning based on artificial neural networks. Differently to other feature learning methods which may be focused on finding specific transformations of the feature space, they can be…

We introduce a machine-learning approach (denoted Symmetry Seeker Neural Network) capable of automatically discovering discrete symmetry groups in physical systems. This method identifies the finite set of parameter transformations that…

Let k be a field of characteristic zero. We consider graded subalgebras A of k[x_1,...,x_m]/(x_1^2,...,x_m^2) generated by d linearly independant linear forms. Representations of matroids over k provide a natural description of the…

The purpose of this paper is to propose an efficient method to compute the automorphism group of an arbitrary hyperelliptic function field (genus>1) over a given ground field of characteristic >2 as well as over its algebraic extensions.