Mathematics and Statistics Colloquium
Title: Unital Shelves
Abstract: A 'shelf' is a set equipped with a single binary operation whose single axiom of self-distributivity,
(x*y)*z = (x*z) *(y*z)
algebraically encodes the third Reidemeister move from classical knot theory. A 'unital shelf' has the additional structure of an element '1' that satisfies x*1 = x and 1*x = x. Surprisingly, it turns out that the shelf operation for unital shelves is associative! We will explore properties of unital shelves in this preliminary work with Mukherjee and Przytycki.