A categorification of the Casimir of quantum \(\mathfrak{sl}(2)\) (Q436244)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: A categorification of the Casimir of quantum \(\mathfrak{sl}(2)\) |
scientific article; zbMATH DE number 6059035
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A categorification of the Casimir of quantum \(\mathfrak{sl}(2)\) |
scientific article; zbMATH DE number 6059035 |
Statements
A categorification of the Casimir of quantum \(\mathfrak{sl}(2)\) (English)
0 references
20 July 2012
0 references
categorified quantum group
0 references
graphical calculus
0 references
Casimir element
0 references
universal invariant
0 references
Witten-Reshetikhin-Turaev invariants
0 references
0 references
0 references
The paper under review categorifies the Casimir element, which is the free generator of the centre of \(U_q(\mathfrak{sl}_2)\) as a \(\mathbb{Z}[q,q^{-1}]\)-algebra. This is a first step towards categorification of Lawrence's universal \(\mathfrak{sl}_2\) invariant of knots, within the context of the categorified representation theory of \(U_q(\mathfrak{sl}_2)\).NEWLINENEWLINEThe main technical tool to handle the increased combinatorial complexity seen in such categorified structures is the diagrammatic calculus of a certain categorified algebra introduced by the third author [Adv. Math. 225, No. 6, 3327--3424 (2010; Zbl 1219.17012)].
0 references
