<p>In this chapter we use additionaly functions from the following packages: CoReLG <a href="chapBib.html#biBCoReLG">[DFdG14]</a> and SLA <a href="chapBib.html#biBSLA">[dG]</a>. We will show in detail the split case (for a non-split case you should use algoritm to generate regular subalgebras from <a href="chapBib.html#biBDFG">[DFdG15]</a>). For example, we take <span class="SimpleMath">G=mathfrake_6(6)</span> (tuple "E",6,2 in CoReLG notation). We calculate <var class="Arg">AllZeroDH</var> on it.</p>
There are 4 simple real forms with complexification A4
1 is of type su(5), compact form
2 - 3 are of type su(p,5-p) with 1 <= p <= 2
4 is of type sl(5,R)
Index '0' returns the realification of A4
<p>Number 14 is in output of <var class="Arg">AllZeroDH</var> function, so for <span class="SimpleMath">mathfrakg=e_6(6)</span> and <span class="SimpleMath">mathfrakh=mathfraksl(5,R)</span> corresponding homogeneous spaces <span class="SimpleMath">G/H</span> do not have compact Clifford–Klein forms.</p>
There are 7 simple real forms with complexification D5
1 is of type so(10), compact form
2 - 3 are of type so(2p,10-2p) with 1 <= p <= 2
4 is of type so*(10)
5 is of type so(9,1)
6 - 7 are of type so(2p+1,10-2p-1) with 1 <= p <= 2
Index '0' returns the realification of D5
<p>Number 25 is not in output of <var class="Arg">AllZeroDH</var> function, so for <span class="SimpleMath">mathfrakg=e_6(6)</span> and <span class="SimpleMath">mathfrakh=mathfrakso(5,5)</span> our algoritm does not provide a solution to the problem.</p>
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