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<div class="ChapSects" ><a href="chap1_mj.html#X7DD31B407B9402A3" >1 <span class="Heading" >Notation</span ></a>
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<h3>1 <span class="Heading" >Notation</span ></h3>
<p>We use the notation and convention for real Lie algebras as is from CoReLG Package, <a href="chapBib_mj.html#biBCoReLG" >[DFdG14]</a>.</p>
<div class="example" ><pre >
<span class="GAPprompt" >gap></span > <span class="GAPinput" >G:=RealFormById( "E" , 7,3);</span >
<Lie algebra of dimension 133 over SqrtField>
<span class="GAPprompt" >gap></span > <span class="GAPinput" >rankG:=Dimension(CartanSubalgebra(G));</span >
7
<span class="GAPprompt" >gap></span > <span class="GAPinput" >rankRG:=Dimension(CartanSubspace(G));</span >
3
<span class="GAPprompt" >gap></span > <span class="GAPinput" >dimG:=Dimension(G);</span >
133
<span class="GAPprompt" >gap></span > <span class="GAPinput" >P:=CartanDecomposition( G ).P;</span >
<vector space over SqrtField, with 54 generators>
<span class="GAPprompt" >gap></span > <span class="GAPinput" >dimPforG:=Dimension(P);</span >
54
<span class="GAPprompt" >gap></span > <span class="GAPinput" >K:=CartanDecomposition( G ).K;</span >
<Lie algebra of dimension 79 over SqrtField>
<span class="GAPprompt" >gap></span > <span class="GAPinput" >rankK:= Dimension(CartanSubalgebra(K));</span >
7
<span class="GAPprompt" >gap></span > <span class="GAPinput" >dimK:= Dimension(K);</span >
79
</pre ></div >
<p>Classification can be found in Table 9 in <a href="chapBib_mj.html#biBonvin" >[OV90]</a>, p. 312-317.</p>
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