Lie algebras and 3-transpositions

Details Lie algebras and 3-transpositions Lie algebras and 3-transpositions

2011-04-04

arxiv.org/abs/1104.0536v1

Mathematics

Group Theory

23 pages

Scientific paper

We describe a construction of an algebra over the field of order 2 starting
from a conjugacy class of 3-transpositions in a group. In particular, we
determine which simple Lie algebras arise by this construction. Among other
things, this construction yields a natural embedding of the sporadic simple
group $\Fi{22}$ in the group $^2E_6(2)$.

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