An odd categorification of Uq(sl2)U_q (\mathfrak{sl}_2)

  • Alexander P. Ellis

    University of Oregon, Eugene, USA
  • Aaron D. Lauda

    University of Southern California, Los Angeles, United States


We define a 2-category that categorifies the covering Kac–Moody algebra for sl2\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 Z×Z2\mathbb{Z} \times \mathbb{Z}_{2}-grading giving its Grothendieck group the structure of a free module over the group algebra of Z×Z2\mathbb{Z} \times \mathbb Z_2. By specializing the Z2\mathbb{Z}_{2}-action to +1 or to −1, the construction specializes to an “odd” categorification of sl2\mathfrak{sl}_2 and to a supercategorification of osp12\mathfrak{osp}_{1|2}, respectively.

Cite this article

Alexander P. Ellis, Aaron D. Lauda, An odd categorification of Uq(sl2)U_q (\mathfrak{sl}_2). Quantum Topol. 7 (2016), no. 2, pp. 329–433

DOI 10.4171/QT/78