Word equations in simple groups and polynomial equations in simple algebras

What is it about?

In this paper, the authors give a brief survey of recent results on word maps on simple groups and polynomial maps on simple associative and Lie algebras. They focus on the parallelism between these theories, pointing out the main questions as well as their challenges, and providing a rich source of references. They also state new open problems and give new ways for solving older ones. It is a very pleasant survey to read. Reviewed by Marinês Guerreiro

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