Towers of graded superalgebras categorify the twisted Heisenberg double
arXiv:1406.0421 · doi:10.1016/j.jpaa.2015.03.016
Abstract
We show that the Grothendieck groups of the categories of finitely-generated graded supermodules and finitely-generated projective graded supermodules over a tower of graded superalgebras satisfying certain natural conditions give rise to twisted Hopf algebras that are twisted dual. Then, using induction and restriction functors coming from such towers, we obtain a categorification of the twisted Heisenberg double and its Fock space representation. We show that towers of wreath product algebras (in particular, the tower of Sergeev superalgebras) and the tower of nilcoxeter graded superalgebras satisfy our axioms. In the latter case, one obtains a categorification of the quantum Weyl algebra.
29 pages; v2: Minor changes (corrected typos, etc.) throughout
References in corpus (2)
Cited by in corpus (6)
- A general approach to Heisenberg categorification via wreath product algebras
- Affine wreath product algebras
- A graphical calculus for the Jack inner product on symmetric functions
- Twisted Frobenius extensions of graded superrings
- Representation theory of 0-Hecke-Clifford algebras
- Nested Frobenius extensions of graded superrings