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arxiv: 1104.0536 · v1 · pith:ILS54RJYnew · submitted 2011-04-04 · 🧮 math.GR · math.CO· math.RA

Lie algebras and 3-transpositions

H. Cuypers , M. Horn , J. in 't panhuis , S. Shpectorov This is my paper
classification 🧮 math.GR math.COmath.RA
keywords constructiongroupalgebrassimpletranspositionsalgebraariseclass
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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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