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A basis theorem for the affine oriented Brauer category and its cyclotomic quotients. (English) Zbl 1419.18011
Summary: 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.

18D10 Monoidal, symmetric monoidal and braided categories (MSC2010)
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
17B35 Universal enveloping (super)algebras
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