29 citations · 56 across the 15 of their papers we have counts for
7 papers · 1 filter
-graded Lie algebras, cubic norm structures and quadrangular algebras
Tom De Medts, Jeroen Meulewaeter
We study simple Lie algebras generated by extremal elements, over arbitrary fields of arbitrary characteristic. We show: (1) If the extremal geometry contains lines, then the Lie a…
Operator Kantor Pairs
Sigiswald Barbier, Tom De Medts, Michiel Smet
Kantor pairs, (quadratic) Jordan pairs, and similar structures have been instrumental in the study of -graded Lie algebras and algebraic groups. We introduce the notion…
Primitive 4-generated axial algebras of Jordan type
Tom De Medts, Louis Rowen, Yoav Segev
We show that primitive 4-generated axial algebras of Jordan type are at most 81-dimensional.
Modules over axial algebras
Tom De Medts, Michiel Van Couwenberghe
We introduce axial representations and modules over axial algebras as new tools to study axial algebras. All known interesting examples of axial algebras fall into this setting, in…
Jordan algebras and 3-transposition groups
Tom De Medts, Felix Rehren
An idempotent in a Jordan algebra induces a Peirce decomposition of the algebra into subspaces whose pairwise multiplication satisfies certain fusion rules . On the…
A new construction of Moufang quadrangles of type E6, E7 and E8
Lien Boelaert, Tom De Medts
In the classification of Moufang polygons by J. Tits and R. Weiss, the most intricate case is by far the case of the exceptional Moufang quadrangles of type E_6, E_7 and E_8, and i…
Exceptional Moufang quadrangles and structurable algebras
Lien Boelaert, Tom De Medts
In 2000, J. Tits and R. Weiss classified all Moufang spherical buildings of rank two, also known as Moufang polygons. The hardest case in the classification consists of the Moufang…