Khovanov, Mikhail and Sazdanovic, Radmila - A Categorification of One-Variable Polynomials

dmtcs:2468 - Discrete Mathematics & Theoretical Computer Science, January 1, 2015, DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)
A Categorification of One-Variable Polynomials

Authors: Khovanov, Mikhail and Sazdanovic, Radmila

We develop a diagrammatic categorification of the polynomial ring $\mathbb{Z} [x]$, based on a geometrically-defined graded algebra and show how to lift various operations on polynomials to the categorified setting. Our categorification satisfies a version of the Bernstein-Gelfand-Gelfand reciprocity property, with indecomposable projective modules corresponding to $x^n$ and standard modules to $(x -1)^n$ in the Grothendieck ring. This construction generalizes tocategorification of various orthogonal polynomials.


Source : oai:HAL:hal-01337757v1
Volume: DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)
Section: Proceedings
Published on: January 1, 2015
Submitted on: November 21, 2016
Keywords: categorification,diagrammatic algebra,Grothendieck ring,Bernstein-Gelfand reciprocity,crossing less matchings,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]


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