Sporadic isogenies to orthogonal groups
نویسنده
چکیده
SO(p, q) = {g ∈ SLp+q(R) : g>Qg = Q} (where Q = ( 1p 0 0 −1q ) ) SU(2) −→ SO(3) SL2(R) −→ SO(2, 1) SU(2)× SU(2) −→ SO(4) SL2(C) −→ SO(3, 1) SL2(R)× SL2(R) −→ SO(2, 2) Sp∗(2, 0) −→ SO(5) Sp∗(1, 1) −→ SO(4, 1) Sp2(R) −→ SO(3, 2) SU(4) −→ SO(6) SL2(H) −→ SO(5, 1) SU(2, 2) −→ SO(4, 2) SL4(R) −→ SO(3, 3) Thus, these are small examples of spin groups, two-fold covers of special orthogonal groups.
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