- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:39
Quantum Topology
Quantum Topol.
QT
1663-487X
1664-073X
General
10.4171/QT
http://www.ems-ph.org/doi/10.4171/QT
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
7
2016
2
An odd categorification of $U_q (\mathfrak{sl}_2)$
Alexander
Ellis
University of Oregon, EUGENE, UNITED STATES
Aaron
Lauda
University of Southern California, LOS ANGELES, UNITED STATES
Covering algebras, categorified quantum groups, cyclotomic quotients, odd nil-Hecke algebra, odd Khovanov homology
We define a 2-category that categorifies the covering Kac–Moody algebra for $\mathfrak{sl}_2$ introduced by Clark and Wang. This categorification forms the structure of a super-2-category as formulated by Kang, Kashiwara, and Oh. The super-2-category structure introduces a $\mathbb{Z} \times \mathbb{Z}_{2}$-grading giving its Grothendieck group the structure of a free module over the group algebra of $\mathbb{Z} \times \mathbb Z_2$. By specializing the $\mathbb{Z}_{2}$-action to +1 or to −1, the construction specializes to an “odd” categorification of $\mathfrak{sl}_2$ and to a supercategorification of $\mathfrak{osp}_{1|2}$, respectively.
Group theory and generalizations
Nonassociative rings and algebras
Manifolds and cell complexes
329
433
10.4171/QT/78
http://www.ems-ph.org/doi/10.4171/QT/78