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- W4294556799 abstract "Given an imaginary quadratic extension $K$ of $mathbb Q$, we classify the maximal nonelementary subgroups of the Picard modular group $operatorname{PU}(1,2;mathcal O_K)$ preserving a totally real totally geodesic plane in the complex hyperbolic plane $mathbb H^2_mathbb C$. We prove that these maximal $mathbb R$-Fuchsian subgroups are arithmetic, and describe the quaternion algebras from which they arise. For instance, if the radius $Delta$ of the corresponding $mathbb R$-circle lies in $mathbb N-{0}$, then the stabilizer arises from the quaternion algebra $Big(!begin{array}{c} Delta,,, |D_K|hlinemathbb Qend{array} !Big)$. We thus prove the existence of infinitely many orbits of $K$-arithmetic $mathbb R$-circles in the hypersphere of $mathbb P_2(mathbb C)$." @default.
- W4294556799 created "2022-09-04" @default.
- W4294556799 creator A5007467218 @default.
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- W4294556799 date "2017-07-01" @default.
- W4294556799 modified "2023-09-26" @default.
- W4294556799 title "A classification of $mathbb R$-Fuchsian subgroups of Picard modular groups" @default.
- W4294556799 doi "https://doi.org/10.48550/arxiv.1707.00154" @default.
- W4294556799 hasPublicationYear "2017" @default.
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