On discrete subgroups containing a lattice in a horospherical subgroup
Copyright policy )On discrete subgroups containing a lattice in a horospherical subgroup
In the paper under review results from [\textit{H. Oh}, J. Algebra 203, 621-676 (1998; Zbl 0907.22014)] are generalized. The following Theorem is proved: Let \(G\) be a connected absolutely simple \(R\)-split algebraic group with rank at least 2. Suppose that \(G\) is not of type \(A_2\). Let \(\Gamma\) be a discrete Zariski dense subgroup of \(G(R)\). Then \(\Gamma\) is a non-uniform arithmetic lattice in \(G(R)\) if and only if there exists a horospherical \(R\)-subgroup \(U\) of \(G\) such that \(\Gamma \cap U\) is Zariski dense in \(U\).
- Oklahoma State University United States
- Oklahoma State University–Stillwater United States
simple real Lie group, horospherical subgroup, arithmetic lattice, absolutely simple \(R\)-split algebraic group, Discrete subgroups of Lie groups
simple real Lie group, horospherical subgroup, arithmetic lattice, absolutely simple \(R\)-split algebraic group, Discrete subgroups of Lie groups
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