Root group geometries, Lie algebras, and polar spaces
The shadow geometries of spherical buildings corresponding to root nodes
have been characterized as point-line incidence systems in terms of what is
called root filtration spaces. This characterization is useful in that
abstract root groups as introduced by Timmesfeld and simple Lie algebras
over a field char. at least 5 containing an extremal element are easily seen
to lead to root filtrations spaces. I will survey these developments and
focus on two questions of more recent research:
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To what extent is the above Lie algebra structure determined by the
root filtration space?
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Is there a direct proof of the characterization as a root filtration
space of the line Grassmannians of polar spaces?
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