29 citations · 56 across the 15 of their papers we have counts for
19 papers
-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…
Lattice envelopes of right-angled Artin groups
Pierre-Emmanuel Caprace, Tom De Medts
Let be a finite simplicial graph with at least two vertices, and let be the associated right-angled Artin group. We describe a locally compact group contain…
Matsuo algebras in characteristic 2
Tom De Medts, Mathias Stout
We extend the theory of Matsuo algebras, which are certain non-associative algebras related to 3-transposition groups, to characteristic 2. Instead of idempotent elements associate…
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.
Restricted universal groups for right-angled buildings
Jens Bossaert, Tom De Medts
In 2000, Marc Burger and Shahar Mozes introduced universal groups acting on trees. Such groups provide interesting examples of totally disconnected locally compact groups. Intuitiv…
City products of right-angled buildings and their universal groups
Jens Bossaert, Tom De Medts
We introduce the notion of city products of right-angled buildings that produces a new right-angled building out of smaller ones. More precisely, if is a right-angled Coxeter d…
Open subgroups of the automorphism group of a right-angled building
Tom De Medts, Ana C. Silva
We study the group of type-preserving automorphisms of a right-angled building, in particular when the building is locally finite. Our aim is to characterize the proper open subgro…
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…
Tits Endomorphisms and Buildings of Type
Tom De Medts, Yoav Segev, Richard M. Weiss
The fixed point building of a polarity of a Moufang quadrangle of type is a Moufang set, as is the fixed point building of a semi-linear automorphism of order of a Moufan…
Local Moufang sets and local Jordan pairs
Tom De Medts, Erik Rijcken
In this paper, we extend the theory of special local Moufang sets. We construct a local Moufang set from every local Jordan pair, and we show that every local Moufang set satisfyin…
Universal groups for right-angled buildings
Tom De Medts, Ana C. Silva, Koen Struyve
In 2000, M. Burger and S. Mozes introduced universal groups acting on trees with a prescribed local action. We generalize this concept to groups acting on right-angled buildings. W…
Local Moufang sets and PSL_2 over a local ring
Tom De Medts, Erik Rijcken
We introduce local Moufang sets as a generalization of Moufang sets. We present a method to construct local Moufang sets from only one root group and one permutation. We use this t…
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…
Moufang sets of mixed type F4
Elizabeth Callens, Tom De Medts
Moufang sets were introduced by Jacques Tits in order to understand isotropic linear algebraic groups of relative rank one, but the notion is more general. We describe a new class…
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…
Trees, contraction groups, and Moufang sets
Pierre-Emmanuel Caprace, Tom De Medts
We study closed subgroups of the automorphism group of a locally finite tree acting doubly transitively on the boundary. We show that if the stabiliser of some end is metab…
Simple locally compact groups acting on trees and their germs of automorphisms
Pierre-Emmanuel Caprace, Tom De Medts
Automorphism groups of locally finite trees provide a large class of examples of simple totally disconnected locally compact groups. It is desirable to understand the connections b…