5 papers
Inner ideals and structurable algebras: Moufang sets, triangles and hexagons
Tom De Medts, Jeroen Meulewaeter
We construct Moufang sets, Moufang triangles and Moufang hexagons using inner ideals of Lie algebras obtained from structurable algebras via the Tits--Kantor--Koecher construction.…
Topological and algebraic properties of universal groups for right-angled buildings
Jens Bossaert, Tom De Medts
We study universal groups for right-angled buildings. Inspired by Simon Smith's work on universal groups for trees, we explicitly allow local groups that are not necessarily finite…
Decomposition algebras and axial algebras
Tom De Medts, Simon F. Peacock, Sergey Shpectorov +1
We introduce decomposition algebras as a natural generalization of axial algebras, Majorana algebras and the Griess algebra. They remedy three limitations of axial algebras: (1) Th…
Structurable algebras of skew-dimension one and hermitian cubic norm structures
Tom De Medts
We study structurable algebras of skew-dimension one. We present two different equivalent constructions for such algebras: one in terms of non-linear isotopies of cubic norm struct…
Moufang sets arising from polarities of Moufang planes over octonion division algebras
Elizabeth Callens, Tom De Medts
For every octonion division algebra O, there exists a projective plane which is parametrized by O; these planes are related to rank two forms of linear algebraic groups of absolute…