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# Research Group *Algebra*

Members of the research group | |

Tom De Medts (tenured) | Tom.DeMedts@UGent.be |

Jeroen Demeyer (postdoc, currently on Horizon 2020 project "OpenDreamKit") | jdemeyer@cage.UGent.be |

Wouter Castryck (postdoc) | Wouter.Castryck@UGent.be |

Andrew Dolphin (postdoc) | Andrew.Dolphin@UGent.be |

Karsten Naert (PhD student — assistant) | kn@cage.UGent.be |

Ana Filipa Costa Da Silva (PhD student — FWO project) | anasilva@cage.UGent.be |

Erik Rijcken (PhD student — FWO fellowship) | erijcken@cage.UGent.be |

Michiel Van Couwenberghe (PhD student — FWO fellowship) | Michiel.VanCouwenberghe@UGent.be |

## Current research topics

Our research deals mainly (but not exclusively) with the connection between group theory and non-associative algebraic structures.

### Moufang sets, structurable algebras and linear algebraic groups

We investigate the connection between a class of non-associative algebras known as *structurable algebras*
and linear algebraic groups (over arbitrary fields) and related group-theoretical structures such as Moufang sets
(this is a class of doubly transitive permutation groups, introduced by Jacques Tits).
In particular, we make use of Jordan algebras, quadratic forms, and other algebraic objects related to linear algebraic groups.
We are particularly interested in exceptional linear algebraic groups.

Many connections with other areas are also explored: model theory (groups of finite Morley rank), finite group theory, incidence geometry (building theory), Lie theory, and so on.

### Finite groups and axial algebras

An *axial algebra* is a commutative non-associative algebra generated by certain idempotents such that the multiplication
of eigenspaces with respect to each idempotent satisfies a certain fusion rule.
The example after which these algebras have been modeled, is the Griess algebra, the automorphism group of which is the Monster group.
We have been investigating connections between axial algebras and 3-transposition groups, and we are currently studying possible
extensions towards other classes of finite groups.

### Totally disconnected locally compact groups

We have been studying automorphism groups of locally finite trees, in particular the so-called universal groups (with respect to a prescribed local action). We have extended this to the study of universal groups for right-angled buildings.