Categorification of quantum Kac-Moody superalgebras

Abstract

We introduce a non-degenerate bilinear form and use it to provide a new characterization of quantum Kac-Moody superalgebras with no isotropic odd simple roots. We show that the spin quiver Hecke algebras introduced by Kang-Kashiwara-Tsuchioka provide a categorification of half the quantum Kac-Moody superalgebras, using the recent work of Ellis-Khovanov-Lauda. A new idea here is that a super sign is categorified as spin (i.e., the parity-shift functor).