Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8896053 | Journal of Algebra | 2018 | 25 Pages |
Abstract
We consider a possible framework to categorify the exponential map expâ¡(âf) given the categorification of a generator f of sl2 by Lauda. In this setup the Taylor expansions of expâ¡(âf) and expâ¡(f) turn into complexes built out of categorified divided powers of f. Hom spaces between tensor powers of categorified f are given by diagrammatics combining nilHecke algebra relations with those for a additional “short strand” generator. The proposed framework is only an approximation to categorification of exponentiation, because the functors categorifying expâ¡(f) and expâ¡(âf) are not invertible.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Mikhail Khovanov, Yin Tian,