A q-Brauer algebra

We define a new $q$-deformation of Brauer's centralizer algebra which contains Hecke algebras of type $A$ as unital subalgebras. We determine its generic structure as well as the structure of certain semisimple quotients. This is expected to have applications for constructions of subfactors of type II$_1$ factors and for module categories of fusion categories of type $A$ corresponding to certain symmetric spaces.

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