An approach to categorification of some small quantum groups

2012/08/31 by Mikhail Khovanov, You Qi · 1 citation
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Categorification #Combinatorics #Computer science #Extension (predicate logic) #Linguistics #Mathematics #Physics #Prime (order theory) #Pure mathematics #Quantum #Quantum group #Quantum mechanics #Root (linguistics) #Root of unity #math.KT #math.QA #math.RT #msc:16E20 #msc:16E35 #msc:81R50

paper · pdf · doi:10.4171/qt/63

published as Quantum Topology, Volume 6, Issue 2, 2015, pp. 185-311 · Latex file, 104 pages, many ps tricks figures. V3 contains minor corrections. Comments welcome

arxiv created 2013/06/17 · openalex publication_date 2015/05/30 · arxiv updated 2016/01/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We categorify one half of the small quantum sl(2) at a prime root of unity. An extension of this construction to an arbitrary simply-laced case is proposed.

Citations

• Instantons on ALE spaces, quiver varieties, and Kac-Moody algebras
• N -Complexes as Functors, Amplitude Cohomology and Fusion Rules
• A diagrammatic approach to categorification of quantum groups II
• Deriving DG categories
• Canonical Bases Arising from Quantized Enveloping Algebras

Cited by

• The Center of Small Quantum Groups I: The Principal Block in Type A