Related papers: Albert's twisted field construction using division…
Higgs algebras are used to construct rotational Hamiltonians. The correspondence between the spectrum of a triaxial rotor and the spectrum of a cubic Higgs algebra is demonstrated. It is shown that a suitable choice of the parameters of the…
For certain problems involving vector fields, it is possible to find an associated imaginary field that, in conjunction with the first, forms a complex field for which the equation can be solved. This result is generalized to arbitrary…
A finite-dimensional unital and associative algebra over $\mathbb{R}$, or what we shall call simply "an algebra" in this paper for short, generalities the construction by which we derive the complex numbers by "adjoining an element $i$" to…
For any double Poisson algebra, we produce a double Poisson vertex algebra using the jet algebra construction. We show that this construction is compatible with the representation functor which associates to any double Poisson (vertex)…
Starting from some ideas given by Bales in [Ba; 09], in this paper we present an algorithm for computing the elements of the basis in an algebra obtained by the Cayley-Dickson process. As a consequence of this result, we prove that an…
A method to construct trihamiltonian extensions of a separable system is presented. The procedure is tested for systems, with a natural Hamiltonian, separable in classical sense in one of the four orthogonal separable coordinate systems of…
Linear algebra is usually defined over a field such as the reals or complex numbers. It is possible to extend this to skew fields such as the quaternions. However, to the authors' knowledge there is no commonly accepted notation of linear…
Any cluster-tilted algebra is the relation extension of a tilted algebra. We present a method to, given the distribution of a cluster-tilting object in the Auslander-Reiten quiver of the cluster category, construct all tilted algebras whose…
The split quartic Cayley algebra is a structurable algebra which has been used to give constructions of Lie algebras of type D4. Here, we calculate its group of automorphisms, its algebra of derivations and its gradings.
This paper is devoted to survey composition algebras and some of their applications. After overviewing the classical algebras of quaternions and octonions, both unital composition algebras (or Hurwitz algebras) and symmetric composition…
We construct integral forms for the universal enveloping algebras of certain twisted multiloop algebras and explicit integral bases for these integral forms.
We study holonomy algebras generated by an algebraic element of the Clifford algebra, or equivalently, the holonomy algebras of certain spin connections in flat space. We provide series of examples in arbitrary dimensions and establish…
We study systems of quadratic forms over fields and their isotropy over 2-extensions. We apply this to obtain particular splitting fields for quaternion algebras defined over a finite field extension. As a consequence, we obtain that every…
We construct a version of Fourier transform for a class of non-commutative algebras over abelian varieties which include algebras of twisted differential operators generalizing the previous construction of Laumon (alg-geom/9603004) and of…
A simple sufficient condition for certain cyclic algebras of odd degree d to be split is presented. It employs certain binary forms of degree d and the values they represent. A similar sufficient condition for certain Albert algebras not to…
G. Prasad and A. Rapinchuk asked if two quaternion division F -algebras that have the same subfields are necessarily isomorphic. The answer is known to be "no" for some very large fields. We prove that the answer is "yes" if F is an…
This paper is dedicated to the memory of Zbigniew Oziewicz, to his generosity, intelligence and intensity in the search that is science and mathematics. The paper begins with a basic construction that produces Clifford algebras inductively,…
We give sufficient conditions for the descent construction to be the universal central extension of a twisted form of a split simple Lie algebra over a ring. In particular, the universal central extensions of twisted multiloop Lie tori are…
The connection of (split-)division algebras with Clifford algebras and supersymmetry is investigated. At first we introduce the class of superalgebras constructed from any given (split-)division algebra. We further specify which real…
This paper classifies the derivations of twisted group algebras in terms of the generators and defining relations of the group. In particular, we generalize some know results over group algebras to the case of twisted group algebras. We…