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- W1580180029 abstract "We give an explicit construction of the simply-connected compact real form of the Lie group of type <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper E 7> <mml:semantics> <mml:msub> <mml:mi>E</mml:mi> <mml:mn>7</mml:mn> </mml:msub> <mml:annotation encoding=application/x-tex>E_7</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, as a group of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=28 times 28> <mml:semantics> <mml:mrow> <mml:mn>28</mml:mn> <mml:mo>Γ<!-- Γ --></mml:mo> <mml:mn>28</mml:mn> </mml:mrow> <mml:annotation encoding=application/x-tex>28times 28</mml:annotation> </mml:semantics> </mml:math> </inline-formula> matrices over quaternions, acting on a <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=28> <mml:semantics> <mml:mn>28</mml:mn> <mml:annotation encoding=application/x-tex>28</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-dimensional left quaternion vector space. This leads to a description of the simply-connected split real form, acting on a <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=56> <mml:semantics> <mml:mn>56</mml:mn> <mml:annotation encoding=application/x-tex>56</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-dimensional real vector space, and thence to the finite quasi-simple groups of type <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper E 7> <mml:semantics> <mml:msub> <mml:mi>E</mml:mi> <mml:mn>7</mml:mn> </mml:msub> <mml:annotation encoding=application/x-tex>E_7</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. The sign problems usually associated with constructing exceptional Lie groups are almost entirely absent from this approach." @default.
- W1580180029 created "2016-06-24" @default.
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- W1580180029 date "2013-12-26" @default.
- W1580180029 modified "2023-09-23" @default.
- W1580180029 title "A quaternionic construction of πΈβ" @default.
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- W1580180029 doi "https://doi.org/10.1090/s0002-9939-2013-11838-1" @default.
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