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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.

MSC:
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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