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 $I$ 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.

51 pages; made small corrections, update the references

References in corpus (3)

• 2-Kac-Moody algebras
• Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras
• Categorification of Highest Weight Modules via Khovanov-Lauda-Rouquier Algebras

Cited by in corpus (14)

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• The odd nilHecke algebra and its diagrammatics
• Quantum Supergroups III. Twistors
• An odd categorification of quantum sl(2)
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• Supercategorification of quantum Kac-Moody algebras II
• Oddification of the cohomology of type A Springer varieties
• Quantum supergroups II. Canonical basis
• Quantum Supergroups I. Foundations
• Representation type of finite quiver Hecke algebras of type $A_{2\ell }^{(2)}$
• A cellular approach to the Hecke-Clifford superalgebra
• Super Morita Theory
• A geometric setting for quantum osp(1|2)
• Quantum supergroups IV. The modified form