English

Quiver Hecke superalgebras

Quantum Algebra 2013-03-19 v2 Representation Theory

Abstract

We introduce a new family of superalgebras which should be considered as a super version of the Khovanov-Lauda-Rouquier algebras. Let II 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.

Keywords

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

R2 v1 2026-06-21T18:32:42.837Z