arXiv subjects

Erik Rijcken

Publications and source records attributed to Erik Rijcken.

3 recordsLinked to original sources

arXiv2017

Local Moufang sets

All known Moufang sets arise, in some way or another, from an algebraic structure which can be called `division' in some way. In this PhD dissertation, I made an attempt to develop a theory of local Moufang sets, which generalize Moufang sets in a way to allow constructing using the corresponding local algebraic structures. In the first of the two major parts of the dissertation, I develop the theory of local Moufang sets, while in the second part, some examples are constructed. The most general example constructed arises from a local Jordan pair (which corresponds to a local Jordan algebra), and one of the main theorems characterizes these local Moufang sets.

math.GR↗

arXiv2017

Local Moufang sets and PSL_2 over a local ring

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 to describe $\mathsf{PSL}_2$ over a local ring as a local Moufang set, and give necessary and sufficient conditions for a local Moufang set to be of this form.

math.GR↗

arXiv2016

Local Moufang sets and local Jordan pairs

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 satisfying certain (natural) conditions gives rise to a local Jordan pair. We also explore the connections between these two constructions.

math.GR↗