Expansion in $SL_d(O_K/I)$, $I$ square-free
By P. P. Varj'u. 2010
64 citations recorded by the source corpus.
Let S be a fixed symmetric finite subset of SL_d(O_K) that generates a Zariski dense subgroup of SL_d(O_K) when we consider it as an algebraic group over Q by restriction of scalars. We prove that the Cayley graphs of SL_d(O_K/I) with respect to the projections of S is an expander family if I ranges over square-free ideals of O_K if d=2 and K is an arbitrary numberfield, or if d=3 and K=Q.
Subfields: Algebra and Number Theory, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/2cc14f009da6d7891703a99c828811625c43d221
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In Algebra and Number Theory
In Geometry and Topology
Citations in the corpus
- Random walks in compact groups (2012, background): “The statement of the following theorem is very technical, so we first explain it informally: We suppose that G is a quasirandom profinite group and partition its finite index normal subgroups into two sets: Ω1∪̇Ω2.”