Article ID Journal Published Year Pages File Type
8896053 Journal of Algebra 2018 25 Pages PDF
Abstract
We consider a possible framework to categorify the exponential map exp⁡(−f) given the categorification of a generator f of sl2 by Lauda. In this setup the Taylor expansions of exp⁡(−f) and exp⁡(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 exp⁡(f) and exp⁡(−f) are not invertible.
Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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