### 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 $^2E_6(2)$.

Original language | English |
---|---|

Publisher | s.n. |

Number of pages | 23 |

Publication status | Published - 2011 |

### Publication series

Name | arXiv.org [math.GR] |
---|---|

Volume | 1104.0536 |

## Fingerprint Dive into the research topics of 'Lie algebras and 3-transpositions'. Together they form a unique fingerprint.

## Cite this

Cuypers, H., Horn, M. A. S., Panhuis, in 't, J. C. H. W., & Shpectorov, S. V. (2011).

*Lie algebras and 3-transpositions*. (arXiv.org [math.GR]; Vol. 1104.0536). s.n.