Lie algebras and 3-transpositions
H. Cuypers, M. Horn, J. in 't panhuis, S. Shpectorov

TL;DR
This paper presents a construction linking 3-transpositions in groups to Lie algebras over GF(2), revealing connections to sporadic groups and classical Lie algebras.
Contribution
It introduces a novel algebraic construction from 3-transpositions that characterizes certain simple Lie algebras and embeds sporadic groups into classical groups.
Findings
Identifies which simple Lie algebras can be constructed from 3-transpositions.
Provides a natural embedding of the sporadic group Fi22 into ^2E_6(2).
Establishes a new link between group theory and Lie algebra theory.
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 in the group .
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