Word equations in simple groups and polynomial equations in simple algebras

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.

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• Commutator rings
• Open Problems on Central Simple Algebras
• The yoga of commutators
• Commutator width in Chevalley groups
• On the Surjectivity of Engel Words on PSL(2,q)
• Finitely generated infinite simple groups of infinite commutator width
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• Finitely generated infinite simple groups of infinite square width and vanishing stable commutator length
• About Goto's method showing surjectivity of word maps
• On extension of coverings
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Cited by in corpus (7)

• Evaluations of Noncommutative Polynomials on Algebras: Methods and Problems, and the L'vov-Kaplansky Conjecture
• The images of multilinear polynomials evaluated on $3\times 3$ matrices
• The images of Lie polynomials evaluated on matrices
• Roots and Dynamics of Octonion Polynomials
• The winding invariant
• Automorphisms of the category of finitely generated free groups of the some subvariety of the variety of all groups
• On regular Lie algebras