Geometry of word equations in simple algebraic groups over special fields

N. L. Gordeev, B. Kunyavski, E. B. Plotkin

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


This paper contains a survey of recent developments in the investigation of word equations in simple matrix groups and polynomial equations in simple (associative and Lie) matrix algebras, along with some new results on the images of word maps on algebraic groups defined over special fields: Complex, real, p-adic (or close to such), or finite. Bibliography: 174 titles.

Original languageEnglish
Pages (from-to)753-796
Number of pages44
JournalRussian Mathematical Surveys
Issue number5
StatePublished - Oct 2018

Bibliographical note

Funding Information:
The research of the first author was financially supported by the Ministry of Science and Higher Education of the Russian Federation, project 1.661.2016/1.4. The research of the second and third authors was supported by ISF grant 1623/16 and the Emmy Noether Research Institute for Mathematics. The paper was written when the second author visited the MPIM (Bonn). The authors thank all these institutions. AMS 2010 Mathematics Subject Classification. Primary 20F70, 20G15.

Publisher Copyright:
© 2018 Institute of Physics Publishing. All rights reserved.


  • Linear algebraic group
  • Word map


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