Publicaties
On structure and TKK algebras for Jordan superalgebras Universiteit Gent
Unified products for Jordan algebras. Applications Vrije Universiteit Brussel
Given a Jordan algebra A and a vector space V, we describe and classify all Jordan algebras containing A as a subalgebra of codimension dimk(V) in terms of a non-abelian cohomological type object JA(V,A). Any such algebra is isomorphic to a newly introduced object called unified product A♮V. The crossed/twisted product of two Jordan algebras are introduced as special cases of the unified product and the role of the subsequent problem ...
The factorization problem for Jordan algebras: applications Vrije Universiteit Brussel
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 algebra which factorizes through two given Jordan algebras is isomorphic to a bicrossed product associated to a certain matched pair between the same two Jordan algebras. Furthermore, a new type of ...
Local Moufang sets and local Jordan pairs Universiteit Gent
Point-line spaces related to Jordan pairs Universiteit Gent
Moufang sets and structurable division algebras Universiteit Gent
Algebraic constructions for Jacobi-Jordan algebras Vrije Universiteit Brussel
For a given Jacobi-Jordan algebra A and a vector space V over a field k, a non-abelian cohomological type object HA2(V,A) is constructed: it classifies all Jacobi-Jordan algebras containing A as a subalgebra of codimension equal to dimk(V). Any such algebra is isomorphic to a so-called unified product A♮V. Furthermore, we introduce the bicrossed (semi-direct, crossed, or skew crossed) product A⋈V associated to two Jacobi-Jordan algebras as a ...