An introduction to diagrammatic algebra and categorified quantum sl(2)

Understand

This expository article explains how planar diagrammatics naturally arise in the study of categorified quantum groups with a focus on the categorification of quantum sl2.

• We derive the definition of categorified quantum sl2 and highlight some of the new structure that arises in categorified quantum groups.
• The expert will find a discussion of rescalling isomorphisms for categorified quantum sl2, a proof that cyclotomic quotients of the nilHecke algebra are isomorphic to matrix rings over the cohomology ring of Grassmannians, and an interpretation of `fake bubbles' using symmetric functions.