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no. 5
Frobenius Heisenberg categorification
Savage, Alistair1
1 Department of Mathematics and Statistics University of Ottawa STEM Building 150 Louis-Pasteur Ottawa, Ontario, Canada
Algebraic Combinatorics, Volume 2 (2019) no. 5, pp. 937-967.

We associate a graded monoidal supercategory ℋeis 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 ℋeis 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:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.73
Classification: 18D10, 17B10, 17B65
Keywords: Categorification, graded Frobenius superalgebra, Heisenberg algebra, diagrammatic calculus

Savage, Alistair 1

1 Department of Mathematics and Statistics University of Ottawa STEM Building 150 Louis-Pasteur Ottawa, Ontario, Canada
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Savage, Alistair. Frobenius Heisenberg categorification. Algebraic Combinatorics, Volume 2 (2019) no. 5, pp. 937-967. doi : 10.5802/alco.73. https://alco.centre-mersenne.org/articles/10.5802/alco.73/

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