Related papers: Jordan quadruple systems
We show that a differential algebraic group can be filtered by a finite subnormal series of differential algebraic groups such that successive quotients are almost simple, that is have no normal subgroups of the same type. We give a…
We establish a natural correspondence between (the equivalence classes of) cubic solutions of an eiconal type equation and (the isomorphy classes of) cubic Jordan algebras.
We construct a matrix algebra $\Lambda(A,B)$ from two given finite dimensional elementary algebras $A$ and $B$ and give some sufficient conditions on $A$ and $B$ under which the derived Jordan--H\"older property (DJHP) fails for…
We use principal angles between two subspaces to define Jordan planes. Jordan planes provide an optimal way to decompose $\mathbb{C}^n$ in relation to given two subspaces. We apply Jordan planes to show that two pairs of of subspaces…
We introduce a new approach to the classification of operator identities, based on basic concepts from the theory of algebraic operads together with computational commutative algebra applied to determinantal ideals of matrices over…
Let $\lambda$ be a partition of an integer $n$ and ${\mathbb F}_q$ be a finite field of order $q$. Let $P_\lambda(q)$ be the number of strictly upper triangular $n\times n$ matrices of the Jordan type $\lambda$. It is known that the…
In 1878, Jordan showed that a finite subgroup of GL(n,C) contains an abelian normal subgroup whose index is bounded by a function of n alone. Previously, the author has given precise bounds. Here, we consider analogues for finite linear…
We present a periodic infinite chain of finite generalisations of the exceptional structures, including e8, the exceptional Jordan algebra (and pair), and the octonions. We demonstrate that the exceptional Jordan algebra is part of an…
We construct Jordan algebras over a locally ringed space using generalizations of the Tits process and the first Tits construction by Achhammer. Some general results on the structure of these algebras are obtained. Examples of Albert…
An efficient method is proposed for computing the structure of Jordan blocks of a matrix of integers or rational numbers by exact computation. We have given a method for computing Jordan chains of a matrix with exact computation. However,…
We define a general notion of partially ordered Jordan algebra (over a partially ordered ring), and we show that the Jordan geometry associated to such a Jordan algebra admits a natural invariant partial cyclic order, whose intervals are…
Jordan operator algebras are norm-closed spaces of operators on a Hilbert space with $a^2 \in A$ for all $a \in A$. We study noncommutative topology, noncommutative peak sets and peak interpolation, and hereditary subalgebras of Jordan…
The group-scheme of automorphisms of the ten-dimensional exceptional Kac's Jordan superalgebra is shown to be isomorphic to the semidirect product of the direct product of two copies of SL2 by the constant group scheme C2. This is used to…
The notion of axial algebra is closely related to $3$-transposition groups, the Monster group and vertex operator algebras. In this work we continue our previous works and compete the proof that all algebras generated by a set of primitive…
We present new results about Jordan algebras and Jordan coalgebras, and we discuss about their connections with the Yang-Baxter equations.
We prove that the group of birational automorphisms of a geometrically irreducible algebraic surface over a finite field is Jordan. We show that the analogous statement fails in higher dimensions. Finally, we prove that groups of birational…
We characterise all Jordan triple product homomorphisms, that is, mappings $\Phi$ satisfying $$ \Phi(ABA) = \Phi(A)\Phi(B)\Phi(A) $$ from the set of all Hermitian $n \times n$ complex matrices to the field of complex numbers. Further we…
We describe non-trivial $\delta$-derivations of semisimple finite-dimensional Jordan algebras over an algebraically closed field of characteristic not 2, and of simple finite-dimensional Jordan superalgebras over an algebraically closed…
We give the presentation of exceptional bounded symmetric domains using the Albert algebra and exceptional Jordan triple systems. The first chapter is devoted to Cayley-Graves algebras, the second to exceptional Jordan triple systems. In…
We obtain general upper bounds of the sizes and the numbers of Jordan blocks for the eigenvalues $\lambda \not= 1$ in the monodromies at infinity of polynomial maps.