Ramanujan complexes of type Ãd*

Alexander Lubotzky; Beth Samuels; Uzi Vishne

doi:10.1007/BF02772543

Ramanujan complexes of type Ã_d*

Alexander Lubotzky^*
, Beth Samuels
, Uzi Vishne

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

101 Scopus citations

Abstract

We define and construct Ramanujan complexes. These are simplicial complexes which are higher dimensional analogues of Ramanujan graphs (constructed in [LPS]). They are obtained as quotients of the buildings of type Ã_d-1 associated with PGL_d(F) where F is a local field of positive characteristic.

Original language	English
Pages (from-to)	267-299
Number of pages	33
Journal	Israel Journal of Mathematics
Volume	149
DOIs	https://doi.org/10.1007/BF02772543
State	Published - 2005

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abstract = "We define and construct Ramanujan complexes. These are simplicial complexes which are higher dimensional analogues of Ramanujan graphs (constructed in [LPS]). They are obtained as quotients of the buildings of type {\~A}d-1 associated with PGLd(F) where F is a local field of positive characteristic.",

author = "Alexander Lubotzky and Beth Samuels and Uzi Vishne",

year = "2005",

doi = "10.1007/BF02772543",

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AU - Samuels, Beth

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AB - We define and construct Ramanujan complexes. These are simplicial complexes which are higher dimensional analogues of Ramanujan graphs (constructed in [LPS]). They are obtained as quotients of the buildings of type Ãd-1 associated with PGLd(F) where F is a local field of positive characteristic.

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SN - 0021-2172

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JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

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Ramanujan complexes of type Ã_d*

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