Frobenius Heisenberg categorification
Algebraic Combinatorics, Volume 2 (2019) no. 5, p. 937-967

We associate a graded monoidal supercategory eis F,k to every graded Frobenius superalgebra F and integer k. These categories, which categorify a broad range of lattice Heisenberg algebras, recover many previously defined Heisenberg categories as special cases. In this way, the categories eis F,k serve as a unifying and generalizing framework for Heisenberg categorification. Even in the case of previously defined Heisenberg categories, we obtain new, more efficient, presentations of these categories, based on an approach of Brundan. When k=0, our construction yields new versions of the affine oriented Brauer category depending on a graded Frobenius superalgebra.

Received : 2018-02-12
Revised : 2019-03-08
Accepted : 2019-03-08
Published online : 2019-10-08
DOI : https://doi.org/10.5802/alco.73
Classification:  18D10,  17B10,  17B65
Keywords: Categorification, graded Frobenius superalgebra, Heisenberg algebra, diagrammatic calculus
@article{ALCO_2019__2_5_937_0,
     author = {Savage, Alistair},
     title = {Frobenius Heisenberg categorification},
     journal = {Algebraic Combinatorics},
     publisher = {MathOA foundation},
     volume = {2},
     number = {5},
     year = {2019},
     pages = {937-967},
     doi = {10.5802/alco.73},
     language = {en},
     url = {https://alco.centre-mersenne.org/item/ALCO_2019__2_5_937_0}
}
Frobenius Heisenberg categorification. Algebraic Combinatorics, Volume 2 (2019) no. 5, pp. 937-967. doi : 10.5802/alco.73. https://alco.centre-mersenne.org/item/ALCO_2019__2_5_937_0/

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