Related papers: Differential Central Simple Algebras

Given a central simple algebra with involution over an arbitrary field, \'etale subalgebras contained in the space of symmetric elements are investigated. The method emphasizes the similarities between the various types of involutions and…

We describe relations between maximal subfields in a division ring and in its rational extensions. More precisely, we prove that properties such as being Galois or purely inseparable over the centre generically carry over from one to…

We classify Galois objects for the dual of a group algebra of a finite group over an arbitrary field.

We show that every linear algebraic group over an algebraically closed field of characteristic zero is the differential Galois group of a regular singular linear differential equation with rational function coefficients.

In an attempt to create an algebraic framework for dual canonical bases and total positivity in semisimple groups, we initiate the study of a new class of commutative algebras.

We classify, up to equivalence, all finite-dimensional simple graded division algebras over the field of real numbers. The grading group is any finite abelian group.

The paper is a survey of some results about Weil algebras applicable in differential geometry, especially in some classification questions on bundles of generalized velocities and contact elements. Mainly, a number of claims concerning a…

These notes are a self-contained introduction to Galois theory, designed for the student who has done a first course in abstract algebra.

We give an accessible introduction into the theory of lower central series of associative algebras, exhibiting the interplay between algebra, geometry and representation theory that is characteristic for this subject, and to discuss some…

We state some elementary problems concerning the relation between difference calculus and differential calculus, and we try to convince the reader that, in spite of the simplicity of the statements, a solution of these problems would be a…

These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…

Characteristic Lie algebras of semi-discrete chains are studied. The attempt to adopt this notion to the classification of Darboux integrable chains has been undertaken.

We obtain a Galois correspondence between the lattice of intermediate C*-discrete subalgebras intermediate to a given irreducible C*-discrete inclusion, and characterize these as targets of compatible expectations under a traciality…

In this paper, we focus on derivations and centroids of four dimensional associative algebras. Using an existing classification result of low dimensional associative algebras, we describe the derivations and centroids of four dimensional…

We generalize the solution of linear recurrence relations from fields to central division algebras, adapting the standard tools of companion matrices and characteristic polynomials to the non-commutative setting. We then solve linear…

In this talk we present a division-algebra classification of the generalized supersymmetries admitting bosonic tensorial central charges. We show that for complex and quaternionic supersymmetries a whole class of compatible division-algebra…

Let C be an algebraically closed field and X a projective curve over C. Consider an ordinary linear differential equation, or a linear differ- ence equation, with coefficients in the field of rational functions of X, and assume that its…

Generalized Virasoro algebras (defined as the universal central extension of some generalized Witt algebras) and super-Virasoro algebras and modules of the intermediate series are studied and discussed.

We present here some results of applying the Cayley-Dickson process to certain alternative algebras (notably built upon Galois fields and congruence rings), in a manner which might yield new building blocks for cryptographic systems. We…

The paper presents an algebraic technique for derivation of fast discrete cosine transform (DCT) algorithms. The technique is based on the algebraic signal processing theory (ASP). In ASP a DCT associates with a polynomial algebra…