Lie algebras and 3-transpositions

H. Cuypers; M.A.S. Horn; J.C.H.W. Panhuis, in 't; S.V. Shpectorov

doi:10.1016/j.jalgebra.2012.06.010

Lie algebras and 3-transpositions

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

Discrete Algebra and Geometry

Research output: Contribution to journal › Article › Academic › peer-review

4 Citations (Scopus)

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
Pages (from-to)	21-39
Journal	Journal of Algebra
Volume	368
DOIs	https://doi.org/10.1016/j.jalgebra.2012.06.010
Publication status	Published - 2012

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10.1016/j.jalgebra.2012.06.010

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@article{98386aede99e440185f940f50e3667a3,

title = "Lie algebras and 3-transpositions",

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 $^2E_6(2)$.",

author = "H. Cuypers and M.A.S. Horn and {Panhuis, in 't}, J.C.H.W. and S.V. Shpectorov",

year = "2012",

doi = "10.1016/j.jalgebra.2012.06.010",

language = "English",

volume = "368",

pages = "21--39",

journal = "Journal of Algebra",

issn = "0021-8693",

publisher = "Academic Press Inc.",

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TY - JOUR

T1 - Lie algebras and 3-transpositions

AU - Cuypers, H.

AU - Horn, M.A.S.

AU - Panhuis, in 't, J.C.H.W.

AU - Shpectorov, S.V.

PY - 2012

Y1 - 2012

N2 - 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 $^2E_6(2)$.

AB - 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 $^2E_6(2)$.

U2 - 10.1016/j.jalgebra.2012.06.010

DO - 10.1016/j.jalgebra.2012.06.010

M3 - Article

SN - 0021-8693

VL - 368

SP - 21

EP - 39

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Lie algebras and 3-transpositions

Abstract

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