Lie algebras and 3-transpositions

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

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: Book/Report › Report › Academic

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

Cite this

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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",

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AU - Cuypers, H.

AU - Horn, M.A.S.

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

AU - Shpectorov, S.V.

PY - 2011

Y1 - 2011

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 $^2E_6(2)$.

M3 - Report

T3 - arXiv.org [math.GR]

BT - Lie algebras and 3-transpositions

PB - s.n.

ER -

Lie algebras and 3-transpositions

Abstract

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