A diagrammatic approach to categorification of quantum groups II

By Mikhail Khovanov, Aaron D. Lauda. 2008

221 citations recorded by the source corpus.

To each graph without loops and multiple edges we assign a family of rings. Categories of projective modules over these rings categorify $U^-_q(\mathfrak{g})$, where $\mathfrak{g}$ is the Kac-Moody Lie algebra associated with the graph.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/5a6314553d7babacbe99491e5d3c6d274280f8ba

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In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

An approach to categorification of some small quantum groups II (2012, methodology): “One of the inputs in Webster’s construction is a categorification of positive halves of quantum groups via diagrammatically described KLR rings [20, 21, 41].”
Higher Dimensional Algebra VII: Groupoidification (2009, unknown): “There has been a lot of work attempting to categorify quantum groups, from the early ideas of Crane and Frenkel [11], to the work of Khovanov, Lauda and Rouqier [26, 27, 37], and beyond.”
Nazarov–Wenzl algebras, coideal subalgebras and categorified skew Howe duality (2013, unknown): “This property plays an important role in the context of categorification of modules over quantum groups, [KL09], [Rou08], [BK08], [BS11b].”
A categorification of quantum sl(n) (2008, unknown): “/ in [16], [17], on categories of matrix factorizations that appear in [18, Section 11], etc.”