Word equations in simple groups and polynomial equations in simple algebras

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Abstract

We give a brief survey of recent results on word maps on simple groups and polynomial maps on simple associative and Lie algebras. Our focus is on parallelism between these theories, allowing one to state many new open problems and giving new ways for solving older ones.

Original languageEnglish
Pages (from-to)3-13
Number of pages11
JournalVestnik St. Petersburg University: Mathematics
Volume46
Issue number1
DOIs
StatePublished - 2013

Bibliographical note

Funding Information:
ACKNOWLEDGMENTS This research was supported by the Israel Science Foundation, grant 1207/12. Kunyavskii and Plotkin were supported in part by the Minerva Foundation through the Emmy Noether Research Institute of Mathematics. Some questions raised in this paper were formulated after discussions with N.L. Gordeev, L.H. Rowen, A. Shalev, N.A. Vavilov, and E.I. Zelmanov to whom we are heartily grateful.

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