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Categorifications of the polynomial ring

Volume 230 / 2015

Mikhail Khovanov, Radmila Sazdanovic Fundamenta Mathematicae 230 (2015), 251-280 MSC: Primary 16S99; Secondary 18G10. DOI: 10.4064/fm230-3-3


We develop a diagrammatic categorification of the polynomial ring ${\mathbb {Z}}[x]$. 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.


  • Mikhail KhovanovDepartment of Mathematics
    Columbia University
    2990 Broadway
    509 Mathematics Building
    Mail Code: 4406
    New York, NY 10027, U.S.A.
  • Radmila SazdanovicDepartment of Mathematics
    North Carolina State University
    Box 8205, Raleigh, NC 27695, U.S.A.

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