Related papers: Jordan-H\"older with uniqueness for semimodular se…
Determining the Jordan canonical form of the tensor product of Jordan blocks has many applications including to the representation theory of algebraic groups, and to tilting modules. Although there are several algorithms for computing this…
Johnstone demonstrated that Heyting semilattices form a semi-abelian category via a specific triple of terms. Inspired by this work, we introduce \emph{Johnstone algebras} or J-algebras. The algebraic $(*,\to,e)$-theory $J$ of arities…
We prove that every finite distributive lattice $D$ can be represented as the congruence lattice of a rectangular lattice $K$ in which all congruences are principal. We verify this result in a stronger form as an extension theorem.
A 1955 result of J.~Jakub\'i k states that for the prime intervals $\fp$ and $\fq$ of a finite lattice, $\con{\fp} \geq \con{\fq}$ if{}f $\fp$ is congruence-projective to~$\fq$ (\emph{via} intervals of arbitrary size). The problem is how to…
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 prove a generalization of the Jordan canonical form theorem for a class of bounded linear operators on complex separable Hilbert spaces.
This paper provides new, relatively simple proofs of some important results about unipotent classes in simple linear algebraic groups. We derive the formula for the Jordan blocks of the Richardson class of a parabolic subgroup of a…
The Jacobson Coordinatization Theorem describes the structure of unitary Jordan algebras containing the algebra $H_n(F)$ of symmetric nxn matrices over a field F with the same identity element, for $n\geq 3$. In this paper we extend the…
We provide a simple proof of the Holonomy Theorem using a new Lyndon-Chiswell length function on the Karnofsky-Rhodes expansion of a semigroup. Unexpectedly, we have both a left and a right action on the Chiswell tree by elliptic maps.
The aim of this article is to introduce the concept of centrally-extended Jordan endomorphisms and proving that if $R$ is a non-commutative prime ring of characteristic not two, and $G$ is a CE- Jordan epimorphism such that $[G(x), x] \in…
Recent work in Dynamical Sampling has been centered on characterizing frames obtained by the orbit of a vector under a bounded operator. We prove a necessary and sufficient condition for a pair of bounded commuting operators on a separable…
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…
In this article, we introduce the concepts of higher {g_n, h_n}-derivation and Jordan higher {g_n, h_n}-derivation, and then we give a characterization of higher {g_n, h_n}-derivations in terms of {g, h}-derivations. Using this result, we…
It is, by now, classical that lattices in higher rank semisimple groups have various rigidity properties. In this work, we add another such rigidity property to the list: uniform stability with respect to the family of unitary operators on…
A classical result of Conway and Pless is that a natural projection of the fixed code of an automorphism of odd prime order of a self-dual binary linear code is self-dual. In this paper we prove that the same holds for involutions under…
We investigate endomorphism semirings of a finite semilattice with one least element and one greatest element such that all the other elements form an antichain. We construct some new finite simple semirings. Keywords: endomorphism…
Two semigroups are lattice isomorphic if the lattices of their subsemigroups are isomorphic, and a class of semigroups is lattice closed if it contains every semigroup which is lattice isomorphic to some semigroup from that class. An…
Let $H$ be a transfer Krull monoid over a finite ablian group $G$ (for example, rings of integers, holomorphy rings in algebraic function fields, and regular congruence monoids in these domains). Then each nonunit $a \in H$ can be written…
A theorem of Hukuhara, Levelt, and Turrittin states that every formal differential operator has a Jordan decomposition. This theorem was generalised by Babbit and Varadarajan to the case of formal $G$-connections where $G$ is a semisimple…
A semigroup $S$ is said to be right pseudo-finite if the universal right congruence can be generated by a finite set $U\subseteq S\times S$, and there is a bound on the length of derivations for an arbitrary pair $(s,t)\in S\times S$ as a…