
Conference: Symposium on Mathematical Physics
New aspects of the YangBaxter equation
Dr. Victoria Lebed's talk Date: 10.11.14 Time: 14.00  15.00 Room: Y27H28
The YangBaxter equation (YBE) is omnipresent in modern physics and
mathematics. Its realm includes statistical mechanics, quantum field
theory, differential equations, quantum group theory, lowdimensional
topology. In this talk we will present two new avatars of the YBE,
bringing to light its unifying roles in algebra and in algebraic
homology.
Firstly, we will interpret associativity, Leibniz identity,
selfdistributivity, and some other recurrent algebraic identities as
particular cases of the YBE, and discuss representation and
knottheoretic applications of this interpretation. Secondly, we will
present a homology theory for solutions to the YBE. It generalizes
several familiar homology theories, and serves as a guideline for
developing new ones, which we will see on an example arising in
handlebodyknot theory. Our constructions are of a diagrammatic
nature, which considerably simplifies technical calculations, common
in homology.

