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Russian Mathematical Surveys, 2018, Volume 73, Issue 5, Pages 753–796
DOI: https://doi.org/10.1070/RM9838 (Mi rm9838) 		 
This article is cited in 16 scientific papers (total in 16 papers)

Geometry of word equations in simple algebraic groups over special fields

N. L. Gordeevab, B. È. Kunyavskiĭc, E. B. Plotkinc

a Herzen State Pedagogical University, St. Petersburg, Russia
b St. Petersburg State University
c Bar-Ilan University, Ramat Gan, Israel
English version PDF (911 kB) Citations (16)
References:
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DOI: https://doi.org/10.1070/RM9838
Abstract: 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.
Keywords: linear algebraic group, word map.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 1.661.2016/1.4
Israel Science Foundation 1623/16
Emmy Noether Mathematical Institute
Max-Planck-Institut für Mathematik
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.
Received: 26.06.2018
Russian version:
Uspekhi Matematicheskikh Nauk, 2018, Volume 73, Issue 5(443), Pages 3–52
DOI: https://doi.org/10.4213/rm9838
Bibliographic databases:
Document Type: Article
UDC: 512.7
MSC: 20F70, 20G15
Language: English
Original paper language: Russian
Citation: N. L. Gordeev, B. È. Kunyavskiǐ, E. B. Plotkin, “Geometry of word equations in simple algebraic groups over special fields”, Uspekhi Mat. Nauk, 73:5(443) (2018), 3–52; Russian Math. Surveys, 73:5 (2018), 753–796
Citation in format AMSBIB
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    • This publication is cited in the following 16 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    English version PDF:46
    References:80
    First page:50
     
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