A Categorification of Quantum sl_2

By Wang Zhi. 2011

56 citations recorded by the source corpus.

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A categorification of quantum sl(n) (2008, unknown): “One can check that ̨ (1) ̨ D IdEi 0Ci ii 00 1 and that ̨ ̨ 1 D IdEi 0 iCii 00 1 ̊Œhi; i 1 using the sl2-relations (for details see [21]).”
Generalized trace and modified dimension functions on ribbon categories (2010, background): “The notion of 2-categories have recently received a great deal of attention in representation theory due to work of Khovanov and Lauda [42, 36, 37, 38] and Rouquier [50] in their study of categorification of quantum groups and their representations.”
A diagrammatic approach to categorification of quantum groups II (2008, unknown): “Partially inspired by [9] and [10], the second author suggested and investigated a categorification of Lusztig’s idempotent completion U̇ of quantum sl(2) in [28], [29].”
Quiver Hecke Algebras and 2-Lie Algebras (2011, unknown): “Khovanov and Lauda have constructed a related 2-category and shown that the canonical morphism from the integral form of Uq(g) to the K0 is an isomorphism in type An [22, 16].”
Implicit structure in 2-representations of quantum groups (2011, methodology): “Extending results from [9, 1] an action of the 2category U(sl2) was constructed on categories of modules of cohomology rings [17] (as well as equivariant cohomology rings [18]) of partial flag varieties.”