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Project

Rank one groups over local rings

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.

Date:1 Oct 2013 →  30 Sep 2017
Keywords:Jordan algebras, rank one groups, congruence subgroups, Moufang sets
Disciplines:General mathematics, Mathematical software, Non-associative rings and algebras, Group theory and generalisations, Geometry, Topological groups, Lie groups