Related papers: A Note on the Jordan Canonical Form
We present canonical forms for all indecomposable pairs $(A,B)$ of commuting nilpotent matrices over an arbitrary field under simultaneous similarity, where $A$ is the direct sum of two Jordan blocks with distinct sizes. We also provide the…
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.
We discuss whether the Jordan degree type encodes \break more information about graded artinian Gorenstein algebras than the Jordan type for linear forms. We show that in codimension two, the Jordan type determines the Jordan degree type.…
A conjecture for the dimension and the character of the homogenous components of the free Jordan algebras is proposed. As a support of the conjecture, some numerical evidences are generated by a computer and some new theoretical results are…
In this article, we first give a short introduction to conformal algebras. Then we present three families of simple conformal algebras finite growth generated by simple Jordan algebras of types A, B, C.
Quadratic Jordan algebras are defined by identities that have to hold strictly, i.e that continue to hold in every scalar extension. In this paper we show that strictness is not required for quadratic Jordan division algebras.
We give a rigorous proof of Conjecture 3.1 by Prosen [Prosen T 2010 J. Stat. Mech. $\textbf{2010}$ P07020] on the nilpotent part of the Jordan decomposition of a quadratic fermionic Liouvillian. We also show that the number of the Jordan…
There exists a generalization of the concept, completely bounded norm for multilinear maps on C*-algebras. We will use the word, Jordan norm, for this norm. The Jordan norm of a multilinear map is obtained via factorizations of the map,…
In this paper, we compute all possible Jordan types of linear forms $\ell$ in any full Perazzo algebra $A$. In some cases we are also able to compute the corresponding Jordan degree type, which is a finer invariant.
In this paper, we classify Jordan superalgebras of dimension up to three over an algebraically closed field of characteristic different of two. Our main motivation to obtain such classification comes out from the intention to give an answer…
In this note we mainly study the fine Jordan-Chevalley decomposition: a refinement of the classical Jordan-Chevalley decomposition of a matrix and we pay a particular attention to the field of the coefficients of the matrix. Moreover we…
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…
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…
Having in mind applications to particle physics we develop the differential calculus over Jordan algebras and the theory of connections on Jordan modules. In particular we focus on differential calculus over the exceptional Jordan algebra…
We obtain the generic real Jordan canonical forms for $n\times n$ matrices with real entries. More precisely, we prove that the set of $n\times n$ real matrices is the union of the closures of $\lfloor n/2\rfloor+1$ sets, which are called…
We provide a discussion of Jordan decompositions in the Lie algebra, and the dual Lie algebra, of a reductive group in as uniform a way as possible. We give a counterexample to the claim that Jordan decompositions on the dual Lie algebra…
We present a construction of a Jordan scheme from an elementary abelian $2$-group of rank $n$ and a $\{1,-1\}$-matrix of order $2^n$ that satisfies a specified condition. We then prove that the orders of matrices with the specified…
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.…
We prove the Jordan curve theorem by generalizing the sweepline algorithm for trapezoidal decomposition of a polygon. Our proof uses Zorn's lemma (or, equivalently the axiom of choice). Though several proofs have been given for the Jordan…
The fundamental identity of quadratic Jordan algebras $Q_{Q_a b} = Q_aQ_bQ_a$ is commonly proven as a consequence of MacDonalds theorem or using more analytic methods. In this short note we give a self-contained purely algebraic proof using…