Quiver Hecke superalgebras

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 a decomposition . To this data, we associate a family of graded superalgebras R , the . When , these algebras are noth...

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Published inJournal für die reine und angewandte Mathematik Vol. 2016; no. 711; pp. 1 - 54
Main Authors Kang, Seok-Jin, Kashiwara, Masaki, Tsuchioka, Shunsuke
Format Journal Article
LanguageEnglish
Published De Gruyter 01.02.2016
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Summary: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 a decomposition . To this data, we associate a family of graded superalgebras R , the . When , these algebras are nothing but the usual Khovanov–Lauda–Rouquier algebras. We then define another family of graded superalgebras RC , the quiver Hecke–Clifford superalgebras, and show that the superalgebras R and RC are weakly Morita superequivalent to each other. Moreover, we prove that the affine Hecke–Clifford superalgebras, as well as their degenerate version, the affine Sergeev superalgebras, are isomorphic to quiver Hecke–Clifford superalgebras RC after a completion.
ISSN:0075-4102
1435-5345
DOI:10.1515/crelle-2013-0089