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arXiv · 1202.2769

Categorification of quantum Kac-Moody superalgebras

David Hill·Weiqiang Wang
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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).

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David Hill, Weiqiang Wang. 2012-02-13. Categorification of quantum Kac-Moody superalgebras. https://arxiv.org/abs/1202.2769

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