Quiver Hecke superalgebras
Abstract
We introduce a new family of superalgebras which should be considered as a super version of the Khovanov-Lauda-Rouquier algebras. Let be the set of vertices of a Dynkin diagram with parity. To this data, we associate a family of graded superalgebras, the quiver Hecke superalgebras. When there are no odd vertices, these algebras are nothing but the usual Khovanov-Lauda-Rouquier algebras. We then define another family of graded superalgebras, the quiver Hecke-Clifford superalgebras, and show that they are weakly Morita superequivalent to the quiver Hecke superalgebras. Moreover, we prove that the affine Hecke-Clifford superalgebras, as well as their degenerate version, the affine Sergeev superalgebras, are isomorphic to the quiver Hecke-Clifford superalgebras after a completion.
Cite
@article{arxiv.1107.1039,
title = {Quiver Hecke superalgebras},
author = {Seok-Jin Kang and Masaki Kashiwara and Shunsuke Tsuchioka},
journal= {arXiv preprint arXiv:1107.1039},
year = {2013}
}
Comments
51 pages; made small corrections, update the references