Criteria for equidistribution of solutions of word equations on SL(2)

Tatiana Bandman; Boris Kunyavskiǐ

doi:10.1016/j.jalgebra.2013.02.031

Criteria for equidistribution of solutions of word equations on SL(2)

Tatiana Bandman, Boris Kunyavskiǐ

Department of Mathematics

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

8 Scopus citations

Abstract

We study equidistribution of solutions of word equations of the form w(x,y)=g in the family of finite groups SL(2, q). We provide criteria for equidistribution in terms of the trace polynomial of w. This allows us to get an explicit description of certain classes of words possessing the equidistribution property and show that this property is generic within these classes.

Original language	English
Pages (from-to)	282-302
Number of pages	21
Journal	Journal of Algebra
Volume	382
DOIs	https://doi.org/10.1016/j.jalgebra.2013.02.031
State	Published - 5 May 2013

Bibliographical note

Funding Information:
The authors were supported in part by the Minerva Foundation through the Emmy Noether Research Institute for Mathematics. Kunyavski˘ı was supported in part by grant 1207/12 of the Israel Science Foundation. A part of the work was done during the visit of the second author to the MPIM (Bonn). Support of these institutions is gratefully appreciated.

Funding

The authors were supported in part by the Minerva Foundation through the Emmy Noether Research Institute for Mathematics. Kunyavski˘ı was supported in part by grant 1207/12 of the Israel Science Foundation. A part of the work was done during the visit of the second author to the MPIM (Bonn). Support of these institutions is gratefully appreciated.

Funders	Funder number
Emmy Noether Research Institute for Mathematics	1207/12
Minerva Foundation
Israel Science Foundation

Keywords

Equidistribution
Finite group of Lie type
Trace polynomial
Word map

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10.1016/j.jalgebra.2013.02.031

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abstract = "We study equidistribution of solutions of word equations of the form w(x,y)=g in the family of finite groups SL(2, q). We provide criteria for equidistribution in terms of the trace polynomial of w. This allows us to get an explicit description of certain classes of words possessing the equidistribution property and show that this property is generic within these classes.",

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Criteria for equidistribution of solutions of word equations on SL(2)

Abstract

Bibliographical note

Funding

Keywords

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