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Mon, 13 Oct 2025
16:45
L5

Varieties over free associative algebras

Zlil Sela
Abstract
In the 1960s and 1970s ring theorists (P. M. Cohn, G.Bergman and others) tried to study the structure of sets of solutions to systems of (polynomial) equations (varieties) over free associative algebras. They found significant pathologies that demonstrated the difficulty to achieve their goal.
 
In an ongoing joint work with A. Atkarskaya we modify techniques that were used to study varieties over free groups and semigroups to study the structure of varieties over associative algebras. Along the way we find new structures also in free groups and semigroups.