Dimension expanders

Alexander Lubotzky, Efim Zelmanov*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

Abstract

We show that there exists k ∈ N and 0 < ε{lunate} ∈ R such that for every field F of characteristic zero and for every n ∈ N, there exist explicitly given linear transformations T1, ..., Tk : Fn → Fn satisfying the following: For every subspace W of Fn of dimension less or equal frac(n, 2), dim (W + ∑i = 1k Ti W) ≥ (1 + ε{lunate}) dim W. This answers a question of Avi Wigderson [A. Wigderson, A lecture at IPAM, UCLA, February 2004]. The case of fields of positive characteristic (and in particular finite fields) is left open.

Original languageEnglish
Pages (from-to)730-738
Number of pages9
JournalJournal of Algebra
Volume319
Issue number2
DOIs
StatePublished - 15 Jan 2008

Keywords

  • Expander
  • Property τ
  • Property T

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