Related papers: Albert's twisted field construction using division…
We present a generalization of the notion of an algebra norm relevant to real finite-dimensional unital associative algebras. Among other things, this leads to a novel set of algebra isomorphism invariants, some of which are computationally…
A family of algebras $\mathcal{E}_n$ that extends the Lie algebra of the Drinfel'd double is proposed. This allows us to systematically construct the generalized frame fields $E_A{}^I$ which realize the proposed algebra by means of the…
We consider the concept of fractons, i.e. particles or quasiparticles which obey specific fractal distribution function and for each universal class h of particles we obtain a fractal-deformed Heisenberg algebra. This one takes into account…
We give an explicit description of the Lie algebra of derivations for a class of infinite dimensional algebras which are given by \'etale descent. The algebras under consideration are twisted forms of central algebras over rings, and…
The tensor product of the division algebras, which is a kernel for the structure of the Standard Model, is also a root for the Clifford algebra of (1,9)-space-time. A conventional Dirac Lagrangian, employing the (1,9)-Dirac operator acting…
We study the subfields of quaternion algebras that are quadratic extensions of their center in characteristic 2. We provide examples of the following: two non-isomorphic quaternion algebras that share all their quadratic subfields, two…
The twistor construction is applied for obtaining examples of generalized complex structures (in the sense of N. Hitchin) that are not induced by a complex or a symplectic structure.
Hom-algebras are generalizations of algebras obtained using a twisting by a linear map. But there is a priori a freedom on where to twist. We enumerate here all the possible choices in the Lie and associative categories and study the…
We describe the role of algebraic extensions in the theory of commutative, unital normed algebras, with special attention to uniform algebras. We shall also compare these constructions and show how they are related to each other.
In this paper, we will introduce a novel method for constructing numerous examples of twisted partial Hopf actions. Utilizing split quaternions, split semi-quaternions, and ${1\over4}$-quaternions as our subjects of study, we have obtained…
We construct the well-known decomposition of the Lie algebra $\mathfrak{e}_8$ into representations of $\mathfrak{e}_6\oplus\mathfrak{su}(3)$ using explicit matrix representations over pairs of division algebras. The minimal representation…
To what extent does the maximal subfield spectrum of a division algebra determine the isomorphism class of that algebra? It has been shown that over some fields a quaternion division algebra's isomorphism class is largely if not entirely…
We construct functorially a class of algebras using the formalism of double derivations. These algebras extend to higher dimensions Crawley-Boevey and Holland's construction of deformed preprojective algebras and encompass symplectic…
An extension of the General Coordinate Transformations algebra is constructed by means geometrical consistency conditions. An class of infinite invariants is derived. In particular we construct the consistent extension of the gravitational…
In this paper, we introduce an algebra structure denoted by InvDer algebra whose which we twist an algebra thanks to an invertible derivation, where its inverse is also a derivation. We define InvDer Lie algebras, InvDer associated…
We classify the algebraic combinatorial geometries of arbitrary field extensions of transcendence degree greater than 4 and describe their groups of automorphisms. Our results and proofs extend similar results and proofs by Evans and…
Let p and q be two positive primes. In this paper we obtain a complete characterization of quaternion division algebras H_K(p,q) over the composite K of n quadratic number fields. Also, in Section 6, we obtain a characterization of…
In this paper we address the celebrated Albert problem for exceptional Jordan algebras (i.e. Albert algebras): Does every Albert division algebra contain a cubic cyclic subfield? We prove that for any Albert division algebra $A$ over a…
The octonions are the largest of the four normed division algebras. While somewhat neglected due to their nonassociativity, they stand at the crossroads of many interesting fields of mathematics. Here we describe them and their relation to…
We explain the orthogonal planes split (OPS) of quaternions based on the arbitrary choice of one or two linearly independent pure unit quaternions $f,g$. Next we systematically generalize the quaternionic Fourier transform (QFT) applied to…