# Expansion in $S{L}_{d}({\mathcal{O}}_{K}/I)$, $I$ square-free

Journal of the European Mathematical Society (2012)

- Volume: 014, Issue: 1, page 273-305
- ISSN: 1435-9855

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topVarjú, Péter P.. "Expansion in $SL_d(\mathcal {O}_K/I)$, $I$ square-free." Journal of the European Mathematical Society 014.1 (2012): 273-305. <http://eudml.org/doc/277680>.

@article{Varjú2012,

abstract = {Let $S$ be a fixed symmetric finite subset of $SL_d(\mathcal \{O\}_K)$ that generates a Zariski dense subgroup of $SL_d(\mathcal \{O\}_K)$ when we consider it as an algebraic group over $mathbb Q$ by restriction of scalars. We prove that the Cayley graphs of $SL_d(\mathcal \{O\}_K/I)$ with respect to the projections of $S$ is an expander family if $I$ ranges over square-free ideals of $\mathcal \{O\}_K$ if $d=2$ and $K$ is an arbitrary numberfield, or if $d=3$ and $K=\mathbb \{Q\}$.},

author = {Varjú, Péter P.},

journal = {Journal of the European Mathematical Society},

keywords = {expanders; property tau; Cayley graphs; random walks on groups; affine sieve; expanders; property tau; Cayley graphs; random walks on groups; affine sieves; symmetric generating sets; algebraic groups over number fields},

language = {eng},

number = {1},

pages = {273-305},

publisher = {European Mathematical Society Publishing House},

title = {Expansion in $SL_d(\mathcal \{O\}_K/I)$, $I$ square-free},

url = {http://eudml.org/doc/277680},

volume = {014},

year = {2012},

}

TY - JOUR

AU - Varjú, Péter P.

TI - Expansion in $SL_d(\mathcal {O}_K/I)$, $I$ square-free

JO - Journal of the European Mathematical Society

PY - 2012

PB - European Mathematical Society Publishing House

VL - 014

IS - 1

SP - 273

EP - 305

AB - Let $S$ be a fixed symmetric finite subset of $SL_d(\mathcal {O}_K)$ that generates a Zariski dense subgroup of $SL_d(\mathcal {O}_K)$ when we consider it as an algebraic group over $mathbb Q$ by restriction of scalars. We prove that the Cayley graphs of $SL_d(\mathcal {O}_K/I)$ with respect to the projections of $S$ is an expander family if $I$ ranges over square-free ideals of $\mathcal {O}_K$ if $d=2$ and $K$ is an arbitrary numberfield, or if $d=3$ and $K=\mathbb {Q}$.

LA - eng

KW - expanders; property tau; Cayley graphs; random walks on groups; affine sieve; expanders; property tau; Cayley graphs; random walks on groups; affine sieves; symmetric generating sets; algebraic groups over number fields

UR - http://eudml.org/doc/277680

ER -

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