Related papers: Differential calculus on Jordan algebra and Jordan…
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…
A method is proposed for defining an arbitrary number of differential calculi over a given noncommutative associative algebra. As an example the generalized quantum plane is studied. It is found that there is a strong correlation, but not a…
A short introduction to the mathematical methods and technics of differential algebras and modules adapted to the problems of mathematical and theoretical physics is presented.
There have been several propositions for a geometric and essentially non-linear formulation of quantum mechanics. From a purely mathematical point of view, the point of view of Jordan algebra theory might give new strength to such…
A Jordan H\"older theorem is established for derived module categories of piecewise hereditary algebras. The resulting composition series of derived categories are shown to be independent of the choice of bounded or unbounded derived module…
We construct a basis of free unital generalized Poisson superalgebras and a basis of free unital superalgebras of Jordan brackets. Also, we prove the analogue of Farkas' Theorem for PI unital generalized Poisson algebras and PI unital…
We introduce a category of noncommutative bundles. To establish geometry in this category we construct suitable noncommutative differential calculi on these bundles and study their basic properties. Furthermore we define the notion of a…
In this paper, we study the class of Jordan dialgebras. We develop an approach for reducing problems on dialgebras to the case of ordinary algebras. It is shown that straightforward generalizations of the classical Cohn's, Shirshov's, and…
We pose a new algebraic formalism for studying differential calculus in vector bundles. This is achieved by studying various functors of differential calculus over arbitrary graded commutative algebras (DCGCA) and applying this language to…
We investigate the algebro-geometric structure of a novel two-parameter quantum deformation which exhibits the nature of a semidirect or cross-product algebra built upon GL(2) x GL(1), and is related to several other known examples of…
This is an introduction to advanced linear algebra, with emphasis on geometric aspects, and with some applications included too. We first review basic linear algebra, notably with the spectral theorem in its general form, and with the…
Jordan operator algebras are norm-closed spaces of operators on a Hilbert space which are closed under the Jordan product. The discovery of the present paper is that there exists a huge and tractable theory of possibly nonselfadjoint Jordan…
We give the algebraic and geometric classification of complex four-dimensional Jordan superalgebras. In particular, we describe all irreducible components in the corresponding varieties.
We put forward a definition for spectral triples and algebraic backgrounds based on Jordan coordinate algebras. We also propose natural and gauge-invariant bosonic configuration spaces of fluctuated Dirac operators and compute them for…
This work is the first in a series of papers that, among other things, extends the formalism of diolic differential calculus, wherein a new context for obtaining differential calculus in vector bundles was established. Here we provide a…
We consider an integral version of the Freudenthal construction relating Jordan algebras and exceptional algebraic groups. We show how this construction is related to higher composition laws of M.Bhargava in number theory. We propose an…
In this short note we prove that every Jordan derivation of triangular algebras is a derivation.
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…
This paper is meant to be an informal introduction to Quantum Groups, starting from its origins and motivations until the recent developments. We call in particular the attention on the newly descovered relationship among quantum groups,…
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…