Linear representations of random groups

Gady Kozma; Alexander Lubotzky

doi:10.1142/S1664360719500164

Linear representations of random groups

Weizmann Institute of Science, The Hebrew University of Jerusalem

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

Abstract

We show that for a fixed k is an element of N, Gromov random groups with any density d > 0 have no nontrivial degree k representations over any field, a.a.s. This is especially interesting in light of the results of Agol, Ollivier and Wise that when d <1/6 such groups have a faithful linear representation over Q, a.a.s.

Original language	English
Article number	1950016
Number of pages	12
Journal	Bulletin of Mathematical Sciences
Volume	9
Issue number	3
DOIs	https://doi.org/10.1142/S1664360719500164
State	Published - 15 May 2019

Keywords

Bezout Theorem
Random groups
representations

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1142/S1664360719500164License: CC BY

Cite this

@article{fa7bf7be40e64a4cbd3e8dd60980e7bd,

title = "Linear representations of random groups",

abstract = "We show that for a fixed k is an element of N, Gromov random groups with any density d > 0 have no nontrivial degree k representations over any field, a.a.s. This is especially interesting in light of the results of Agol, Ollivier and Wise that when d <1/6 such groups have a faithful linear representation over Q, a.a.s.",

keywords = "Bezout Theorem, Random groups, representations",

author = "Gady Kozma and Alexander Lubotzky",

year = "2019",

month = may,

day = "15",

doi = "10.1142/S1664360719500164",

language = "English",

volume = "9",

journal = "Bulletin of Mathematical Sciences",

issn = "1664-3607",

publisher = "World Scientific",

number = "3",

}

TY - JOUR

T1 - Linear representations of random groups

AU - Kozma, Gady

AU - Lubotzky, Alexander

PY - 2019/5/15

Y1 - 2019/5/15

N2 - We show that for a fixed k is an element of N, Gromov random groups with any density d > 0 have no nontrivial degree k representations over any field, a.a.s. This is especially interesting in light of the results of Agol, Ollivier and Wise that when d <1/6 such groups have a faithful linear representation over Q, a.a.s.

AB - We show that for a fixed k is an element of N, Gromov random groups with any density d > 0 have no nontrivial degree k representations over any field, a.a.s. This is especially interesting in light of the results of Agol, Ollivier and Wise that when d <1/6 such groups have a faithful linear representation over Q, a.a.s.

KW - Bezout Theorem

KW - Random groups

KW - representations

UR - https://www.scopus.com/pages/publications/85065706022

U2 - 10.1142/S1664360719500164

DO - 10.1142/S1664360719500164

M3 - Article

SN - 1664-3607

VL - 9

JO - Bulletin of Mathematical Sciences

JF - Bulletin of Mathematical Sciences

IS - 3

M1 - 1950016

ER -

Linear representations of random groups

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this