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.
Bibliographical noteFunding 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.
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- Linear algebraic group
- Word map