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 xⁿ and standard modules to (x-1)ⁿ in the Grothendieck ring.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm230-3-3,
author = {Mikhail Khovanov and Radmila Sazdanovic},
title = {Categorifications of the polynomial ring},
journal = {Fundamenta Mathematicae},
volume = {228},
year = {2015},
pages = {251-280},
zbl = {1335.16016},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm230-3-3}
}
Mikhail Khovanov; Radmila Sazdanovic. Categorifications of the polynomial ring. Fundamenta Mathematicae, Tome 228 (2015) pp. 251-280. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm230-3-3/