Swiss Knots 2011

Knot Theory and Algebra

Lake Thun, May 23-27

Categorification of the polynomial ring

Prof. Dr. Radmila Sazdanovic's talk
Date: 23.05.11   Time: 16.30 - 17.20   Room: Gwatt Zentrum

Coauthor: Mikhail Khovanov

Abstract: We develop a diagrammatic categorification of the polynomial ring Z[x], based on the geometrically defined graded algebra and show how to lift various operations on polynomials to the categorified setting. Our categorification satisfies a version of Bernstein-Gelfand-Gelfand reciprocity property with the indecomposable projective modules corresponding to xn and standard modules to (x-1)n in the Grothendieck ring.