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Categorification of the polynomial ring

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arxiv 1101.0293 v1 pith:EXZ5PMFP submitted 2010-12-31 math.QA

Mikhail Khovanov , Radmila Sazdanovic This is my paper · ORCID
classification math.QA
keywords categorificationringmodulespolynomialbernstein-gelfand-gelfandcorrespondingdevelopdiagrammatic
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abstract

We develop a diagrammatic categorification of the polynomial ring $Z[x]$. Our categorification satisfies a version of Bernstein-Gelfand-Gelfand reciprocity property with the indecomposable projective modules corresponding to $x^n$ and standard modules to $(x-1)^n$ in the Grothendieck ring.

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  1. Representation gaps of rigid planar diagram monoids

    math.RT 2025-05 conditional novelty 6.0 of 10

    Rigid non-pivotal Temperley-Lieb, Motzkin, and planar rook monoids have smaller representation gaps than their pivotal counterparts, making them worse for cryptographic use.

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