An introduction to diagrammatic algebra and categorified quantum sl(2)

By Aaron D. Lauda. 2011

78 citations recorded by the source corpus.

This expository article explains how planar diagrammatics naturally arise in the study of categorified quantum groups with a focus on the categorification of quantum sl2. We derive the definition of categorified quantum sl2 and highlight some of the new structure that arises in categorified quantum groups. The expert will find a discussion of rescalling isomorphisms for categorified quantum sl2, a proof that cyclotomic quotients of the nilHecke algebra are isomorphic to matrix rings over the cohomology ring of Grassmannians, and an interpretation of `fake bubbles' using symmetric functions.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/a477ce4d7587e0d425b6d312bbb30cbd1cae4f17

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In Algebra and Number Theory

In Discrete Mathematics and Combinatorics

In Geometry and Topology

Citations in the corpus

The $\mathfrak{sl}_n$ foam 2-category: a combinatorial formulation of Khovanov-Rozansky homology via categorical skew Howe duality (2014, background): “4One can define the 2-category so that degree zero bubbles are multiplication by arbitrary scalars at the cost of modifying some of the other relations, see for example [34, 41].”
Khovanov homology is a skew Howe 2-representation of categorified quantum sl(m) (2012, background): “They allow us to 2One can define the 2-category so that degree zero bubbles are multiplication by arbitrary scalars at the cost of modifying some of the other relations, see for example [45, 52].”