Categorification of quantum Kac-Moody superalgebras

David Hill; Weiqiang Wang

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Categorification of quantum Kac-Moody superalgebras

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arxiv 1202.2769 v2 pith:JWLMPOGR submitted 2012-02-13 math.QA math.RT

Categorification of quantum Kac-Moody superalgebras

David Hill , Weiqiang Wang This is my paper

classification math.QA math.RT

keywords kac-moodyquantumsuperalgebrascategorificationspinalgebrasbilinearcategorified

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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).

Categorification of quantum Kac-Moody superalgebras

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