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On the definition of Heisenberg category. (English) Zbl 06963903
Summary: We revisit the definition of the Heisenberg category of central charge \(k \in \mathbb{Z}\). For central charge \(-1\), this category was introduced originally by Khovanov, but with some additional cyclicity relations which we show here are unnecessary. For other negative central charges, the definition is due to Mackaay and Savage, also with some redundant relations, while central charge zero recovers the affine oriented Brauer category of Brundan, Comes, Nash and Reynolds. We also discuss cyclotomic quotients.

MSC:
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
18D10 Monoidal, symmetric monoidal and braided categories (MSC2010)
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