Is there any reference for the discrete subgroup of complex orthogonal group SO(n,C)? Any classification or examples?
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3$\begingroup$ Do you want discrete subgroups with finite covolume or only discrete subgroups? In any case, there are many examples; if you want only discrete subgroups, a Schottky construction (ping-pong) gives you plenty. If you ask for lattices, many discrete groups can be constructed as unit groups of quadratic forms over an imaginary quadratic extension; a full classification is possible, if $n\geq 5$. $\endgroup$– VenkataramanaCommented Nov 21, 2014 at 3:11
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$\begingroup$ What is the reference for some detailed discussion either lattice or only discrete subgroup? And what if n=4? $\endgroup$– user42804Commented Nov 21, 2014 at 3:17
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2$\begingroup$ If $n\geq 5$, then all lattices are "arithmetic" and classification arises from Galois cohomology , Hasse principle, etc.You have to see the books of Margulis and of Platonov-Rapinchuk for details. If $n\leq 4$, then there are many more lattices. $\endgroup$– VenkataramanaCommented Nov 21, 2014 at 3:40
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