Ramanujan Complexes of Type A_d

2004/06/10 by Alex Lubotzky, Lubotzky, Alex, Beth Samuels +3
Mathematics · #20E42 #22E55 #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT) #math.GR #math.RT #msc:20E42 #msc:22E55

paper · pdf · doi:10.48550/arxiv.math/0406208

32 pages

arxiv created 2005/01/05 · arxiv updated 2009/12/01

Abstract

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

Related

• Explicit Constructions of Ramanujan Complexes of Type A_d
• Highlights from "The Ramanujan Property for Simplicial Complexes" [arXiv:1605.02664]
• Ramanujan Complexes and High Dimensional Expanders
• The Ramanujan Property for Simplicial Complexes
• The Ramanujan property for regular cubical complexes