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Categorification of quantum Kac-Moody superalgebras


Authors: David Hill and Weiqiang Wang
Journal: Trans. Amer. Math. Soc. 367 (2015), 1183-1216
MSC (2010): Primary 17B37, 20J99
DOI: https://doi.org/10.1090/S0002-9947-2014-06128-X
Published electronically: October 23, 2014
MathSciNet review: 3280041
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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 of anisotropic type. We show that the spin quiver Hecke algebras introduced by Kang, Kashiwara and 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 supersign is categorified as spin (i.e., the parity-shift functor).


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Additional Information

David Hill
Affiliation: Department of Mathematics, University of Virginia, Charlottesville, Virginia 22904
Email: deh4n@virginia.edu

Weiqiang Wang
Affiliation: Department of Mathematics, University of Virginia, Charlottesville, Virginia 22904
Email: ww9c@virginia.edu

DOI: https://doi.org/10.1090/S0002-9947-2014-06128-X
Received by editor(s): February 26, 2013
Received by editor(s) in revised form: March 11, 2013
Published electronically: October 23, 2014
Additional Notes: The research of the second author was partially supported by NSF grant DMS-1101268
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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