Research Explorer

Project

Rank one groups over local rings
Code
3F019713
Duration
01 October 2013 → 30 September 2017
Funding
Regional and community funding: Special Research Fund, Research Foundation - Flanders (FWO)
Research disciplines
  • Natural sciences
    • Group theory and generalisations
    • Non-associative rings and algebras
    • Topological groups, Lie groups
    • General mathematics
    • Geometry
    • Mathematical software
Keywords
Jordan algebras rank one groups congruence subgroups Moufang sets
 
Project description

We characterize the class of linear algebraic groups over local rings via an action on an infinite tree. We generalize the theory of Moufang sets to an axiomatic theory determining those groups. Moreover, we study the normal subgroups of those groups. Each ideal of a local ring gives rise to such a normal subgroup, and the question is whether every normal subgroup arises in this fashion.