Lie algebras and 3-transpositions
arXiv:1104.0536 · doi:10.1016/j.jalgebra.2012.06.010
Abstract
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 .
23 pages