Lie algebras and 3-transpositions

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

Research output: Contribution to journalArticleAcademicpeer-review

1 Citation (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 languageEnglish
Pages (from-to)21-39
JournalJournal of Algebra
Volume368
DOIs
Publication statusPublished - 2012

Fingerprint

Transposition
Lie Algebra
Sporadic Simple Groups
Simple Lie Algebra
Conjugacy class
Thing
Algebra

Cite this

Cuypers, H., Horn, M. A. S., Panhuis, in 't, J. C. H. W., & Shpectorov, S. V. (2012). Lie algebras and 3-transpositions. Journal of Algebra, 368, 21-39. https://doi.org/10.1016/j.jalgebra.2012.06.010
Cuypers, H. ; Horn, M.A.S. ; Panhuis, in 't, J.C.H.W. ; Shpectorov, S.V. / Lie algebras and 3-transpositions. In: Journal of Algebra. 2012 ; Vol. 368. pp. 21-39.
@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.",

}

Cuypers, H, Horn, MAS, Panhuis, in 't, JCHW & Shpectorov, SV 2012, 'Lie algebras and 3-transpositions', Journal of Algebra, vol. 368, pp. 21-39. https://doi.org/10.1016/j.jalgebra.2012.06.010

Lie algebras and 3-transpositions. / Cuypers, H.; Horn, M.A.S.; Panhuis, in 't, J.C.H.W.; Shpectorov, S.V.

In: Journal of Algebra, Vol. 368, 2012, p. 21-39.

Research output: Contribution to journalArticleAcademicpeer-review

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

VL - 368

SP - 21

EP - 39

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

ER -