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The affine oriented Brauer category is a monoidal category obtained from the oriented Brauer category (= the free symmetric monoidal category generated by a single object and its dual) by adjoining a polynomial generator subject to appropriate relations. In this article, we prove a basis theorem for the morphism spaces in this category, as well as for all of its cyclotomic quotients.
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Jonathan Brundan, Jonathan Comes, David Nash, Andrew Reynolds, A basis theorem for the affine oriented Brauer category and its cyclotomic quotients. Quantum Topol. 8 (2017), no. 1, pp. 75–112