Related papers: Jordan algebra in R
Let $J$ be a simple closed curve in $\mathbb R^{k}$ $(k\geq2)$ that is differentiable with non-zero derivative at a point $A_0\in J$. For a tuple of positive reals $a_1,\cdots,a_n$ $(n\geq3)$, each of which is less than the sum of the…
We developed a new proper method for classifying $n$-dimensional derived Jordan algebras, and apply it to the classification of $3$-dimensional derived Jordan algebras. As a byproduct, we have the algebraic classification of $3$-dimensional…
In this short article I introduce the stokes package which provides functionality for working with tensors, alternating forms, wedge products, and related concepts from the exterior calculus. Notation and spirit follow Spivak. Stokes's…
It is known that black hole charge vectors of N=8 and magic N=2 supergravity in four and five dimensions can be represented as elements of Jordan algebras of degree three over the octonions and split-octonions and their Freudenthal triple…
In this article, a new notion of $n$-Jordan homomorphism namely the mixed $n$-Jordan homomorphism is introduced. It is proved that how a mixed $(n+1)$-Jordan homomorphism can be a mixed $n$-Jordan homomorphism and vice versa. By means of…
A $G$-grading on an algebra is called multiplicity free if each homogeneous component of the grading is 1-dimensional, where $G$ is an abelian group. We introduce skew root systems of Lie type and skew root systems of Jordan type…
This work presents a guide for the use of some of the functions of the R package "multiColl" for the detection of near multicollinearity. The main contribution, in comparison to other existing packages in R or other econometric software, is…
We classify decompositions of simple special finite-dimensional Jordan superalgebras over an algebraically closed field of characteristic zero into the sum of two proper simple subsuperalgebras.
This paper is a survey of computational issues in algebraic geometry, with particular attention to the theory of Grobner bases and the regularity of an algebraic variety. 1. A geometric introduction to Grobner bases. 2. An algebraic…
The Jordan type of an element $\ell$ of the maximal ideal of an Artinian k-algebra A acting on an A-module M of k-dimension n, is the partition of n given by the Jordan block decomposition of the multiplication map $m_\ell$ on M. In general…
Algebraic computing in relativity and gravitation dates back more than thirty years, but only relatively recently has hardware of sufficient power to tackle large scale calculations become commonplace. Whereas it is generally understood…
In this paper we briefly discuss \Rings --- an efficient lightweight library for commutative algebra. Polynomial arithmetic, GCDs, polynomial factorization and Gr\"obner bases are implemented with the use of modern asymptotically fast…
With this paper we start a programme aiming at connecting two vast scientific areas: Jordan algebras and representation theory. Within representation theory, we focus on non-compact, real forms of semisimple Lie algebras and groups as well…
stagedtrees is an R package which includes several algorithms for learning the structure of staged trees and chain event graphs from data. Score-based and clustering-based algorithms are implemented, as well as various functionalities to…
Let $X$ be a locally finite partially ordered set (poset), $K$ a field of characteristic not 2, and $I(X,K)$ the incidence algebra over $K$. In this paper, we prove that every Jordan $*$-derivation of $I(X,K)$ is an inner $*$-derivation and…
We initiate the study of modules of constant Jordan type for quantum complete intersections, and prove a range of basic properties. We then show that for these algebras, constant Jordan type is an invariant of Auslander-Reiten components.…
This is the expanded version of my talk at the workshop "Groups of Automorphisms in Birational and Affine Geometry", October 29--November 3, 2012, Levico Terme, Italy. The first section is focused on Jordan groups in abstract setting, the…
Let G be an arbitrary group and let K be a field of characteristic different from 2. We classify the G-gradings on the Jordan algebra of upper triangular matrices of order n over K. It turns out that there are, up to a graded isomorphism,…
The paper surveys the history and state-of-the-art of the study of Jordan homomorphisms.
Jordan geometries are defined as spaces equipped with point reflections depending on triples of points, exchanging two of the points and fixing the third. In a similar way, symmetric spaces have been defined by Loos (Symmetric Spaces I,…