Jakob Jurij Snoj: On Bergman's centralizer theorem and commutativity of centralizers in a coproduct

On Bergman's centralizer theorem and commutativity of centralizers in a coproduct

Jakob Jurij Snoj

Abstract: In this talk, I will discuss the centralizer of a nonscalar element in the coproduct $k\langle X\rangle * k[Y]$ of a free associative algebra and a polynomial algebra over a given field. It turns out this centralizer is commutative, for $k\langle X\rangle$ this is part of Bergman's centralizer theorem. The proof of this fact relies on a reduction given in Bergman's proof and is of combinatorial nature, employing a strict order structure of the coproduct monoid.

The talk will be live and streamed.

Roman Drnovšek and Daniel Smertnig