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Quiver Hecke superalgebras
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abstract
We introduce a new family of superalgebras which should be considered as a super version of the Khovanov-Lauda-Rouquier algebras. Let $I$ 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.
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Cited by 1 Pith paper
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Higher-level degenerate spin affine Hecke superalgebras
Higher-level degenerate spin affine Hecke superalgebras are isomorphic (after Clifford tensor) to higher-level degenerate affine Hecke–Clifford superalgebras, hence Morita superequivalent.
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