The disoriented skein category is defined and shown equivalent to the iquantum Brauer category, serving as an interpolating module category with full incarnation functors to modules over iquantum enveloping algebras.
A basis theorem for the affine oriented Brauer category and its cyclotomic quotients
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abstract
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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The disoriented skein and iquantum Brauer categories
The disoriented skein category is defined and shown equivalent to the iquantum Brauer category, serving as an interpolating module category with full incarnation functors to modules over iquantum enveloping algebras.