相关论文: Generators of Invariants of Two $4 \times 4$ Matri…
We provide an explicit set of algebraically independent generators for the algebra of invariant differential operators on the Riemannian symmetric space associated with $\SL_n(\R)$.
Generative adversarial networks are generative models that are capable of replicating the implicit probability distribution of the input data with high accuracy. Traditionally, GANs consist of a Generator and a Discriminator which interact…
We introduce a class of permutation centralizer algebras which underly the combinatorics of multi-matrix gauge invariant observables. One family of such non-commutative algebras is parametrised by two integers. Its Wedderburn-Artin…
Given a finite group $G$, the invariably generating graph of $G$ is defined as the undirected graph in which the vertices are the nontrivial conjugacy classes of $G$, and two classes are adjacent if and only if they invariably generate $G$.…
The algebraic diversity framework generalizes temporal averaging over multiple observations to algebraic group action on a single observation for second-order statistical estimation. The central open problem in this framework is…
Let $V_n$ be the ${\rm SL}_2$-module of binary forms of degree $n$ and let $V = V_1 \oplus V_3 \oplus V_4$. We show that the minimum number of generators of the algebra $R = \mathbb{C}[V]^{{\rm SL}_2}$ of polynomial functions on $V$…
A general simplicity problem in category theory is proposed. A particular example, the simplest choice of generators of an algebra is specified and illustrated by an example.
We prove that for the mixed $q$-Gaussian algebra $\Gamma_{Q}(H_{\mathbb{R}})$ associated to a real Hilbert space $H_{\mathbb{R}}$ and a real symmetric matrix $Q=(q_{ij})$ with $\sup|q_{ij}|<1$, the generator subalgebra is singular.
We construct an explicit set of algebraically independent generators for the center of the universal enveloping algebra of the centralizer of a nilpotent matrix in the Lie algebra gl_N(C). In particular, this gives a new proof of the…
A generic rectangulation is a partition of a rectangle into finitely many interior-disjoint rectangles, such that no four rectangles meet in a point. In this work we present a versatile algorithmic framework for exhaustively generating a…
We obtain an explicit characterization of the stable points of the action of G=SL(2,C) on the cartesian product G^n by simultaneous conjugation on each factor, in terms of the corresponding invariant functions, and derive from it a simple…
This paper presents algebraic methods for the study of polynomial relative invariants, when the group G formed by the symmetries and relative symmetries is a compact Lie group. We deal with the case when the subgroup H of symmetries is…
We present an algorithmic framework for computing generators for the ring of invariants of an Artin-Schreier curve. We give explicit invariants for almost all Artin-Schreier curves of genus up to~8 in standard form, and for a handful of…
We have used the SmallGroups library of groups, together with the computer algebra systems GAP and Mathematica, to search for groups with a three-dimensional irreducible representation in which one of the group generators has a…
We give a method of representing the modular invariant function by generators of a modular function field.
A problem that is frequently encountered in a variety of mathematical contexts, is to find the common invariant subspaces of a single, or set of matrices. A new method is proposed that gives a definitive answer to this problem. The key idea…
The "2-variable general-$\lambda$-matrix polynomials (2VG$\lambda$MP)" is a new family of matrix polynomials, introduced and studied in this article. These matrix polynomials are constructed using umbral and symbolic methods. We delve into…
The space of n (ordered) points on the projective line, modulo automorphisms of the line, is one of the most important and classical examples of an invariant theory quotient, and is one of the first examples given in any course. Generators…
l-Conformal Galilei algebra, denoted by g{l}{d}, is a non-semisimple Lie algebra specified by a pair of parameters (d,l). The algebra is regarded as a nonrelativistic analogue of the conformal algebra. We derive hierarchies of partial…
A minimal system of homogeneous generating elements of the invariants algebra for the binary form of degree 7 is calculated.