Related papers: Characterization of Jordan centralizers and Jordan…
The question of matrix similarity is a classical one in linear algebra. For a field $\mathbb{F}$ and some positive integer $n \in \mathbb{N}$, one may consider the following problems: 1. Given two matrices $A, B \in \mathrm{GL}(n,…
Arising from the classification of the matrix-roots of a nonnegative imprimitive irreducible matrix, we present results concerning the Jordan chains of an $h$-cyclic matrix. We also present ancillary results applicable to nonnegative…
We present various approaches to J. Herzog's theory of generalized local cohomology and explore its main aspects, e.g., (non-)vanishing results as well as a general local duality theorem which extends, to a much broader class of rings,…
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…
Let $A$ be a Banach algebra with a right identity $u$ such that $uA$ is commutative and semisimple. In this paper, we investigate symmetric bi-derivations of $A$ and detremine their range. We also study symmetric bi-derivations of $A$ with…
Recollements of triangulated categories may be seen as exact sequences of such categories. Iterated recollements of triangulated categories are analogues of geometric or topological stratifications and of composition series of algebraic…
The classical Jordan curve theorem for digital curves asserts that the Jordan curve theorem remains valid in the Khalimsky plane. Since the Khalimsky plane is a quotient space of $\mathbb R^2$ induced by a tiling of squares, it is natural…
We investigate the factorization problem as well as the classifying complements problem in the setting of Jordan algebras. Matched pairs of Jordan algebras and the corresponding bicrossed products are introduced. It is shown that any Jordan…
We consider Jordan curves of the form $\gamma=\cup_{j=1}^n \gamma_j$ on the Riemann sphere for which each $\gamma_j$ is a hyperbolic geodesic in $(\widehat{\mathbb C} \smallsetminus \gamma)\cup \gamma_j$. These Jordan curves are…
As shown by Bonnaf\'e, a step in proving a Jordan decomposition of characters of finite special linear groups is the parametrization of unipotent characters of centralizers of semi-simple elements in projective linear groups. We show the…
Working in infinite dimensional linear spaces, we deal with support for closed sets without interior. We generalize the Convexity Theorem for closed sets without interior. Finally we study the infinite dimensional version of Jordan…
The nontrivial subspaces with primitive coproducts are found in the deformed universal enveloping algebras. They can form carrier spaces for additional Jordanian twists. The latter can be used to construct sequences of twists for algebras…
In this paper the analytic characterization of generalized poles of operator valued generalized Nevanlinna functions (including the length of Jordan chains of the representing relation) is completed. In particular, given a Jordan chain of…
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.
A proof of the Jordan canonical form, suitable for a first course in linear algebra, is given. The proof includes the uniqueness of the number and sizes of the Jordan blocks.
It is known that that the centralizer of a matrix over a finite field depends, up to conjugacy, only on the type of the matrix, in the sense defined by J. A. Green. In this paper an analogue of the type invariant is defined that in general…
We show that every Jordan quadrilateral $Q\subset\mathbb{C}$ contains a disk $D$ so that $\partial D\cap\partial Q$ contains points of three different sides of $Q$. As a consequence, together with some modulus estimates from Lehto and…
Let $W$ be a quasiprojective variety over an algebraically closed field of characteristic zero. Assume that $W$ is birational to a product of a smooth projective variety $A$ and the projective line. We prove that if $A$ contains no rational…
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…
We compute and provide a detailed description on the Jordan constants of the multiplicative subgroup of quaternion algebras over number fields of small degree. As an application, we determine the Jordan constants of the multiplicative…