Root groups in totally disconnected locally compact groups

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The general theme of this proposal concerns totally disconnected, locally compact (tdlc) groups and groups acting on buildings. Over the last two decades tdlc groups have been a very active topic of research. Groups of automorphisms of locally finite buildings form an important family of examples of such groups. RGD-systems are the group theoretical approach to buildings and every RGD-system comes equipped with a root system and a family of root groups. Prof. George Willis introduced a notion of roots and root groups in general tdlc groups, which can be seen as analogues of the root system and the root groups of RGD-systems of a special (i.e. spherical) type. In this project we will investigate the connection between the two notions of roots and root groups of general RGD-systems and we will try to find out to what extent properties of the root groups in RGD-systems generalize to the root groups in arbitrary tdlc groups.