2025/05/12 by Peter Schauenburg, Schauenburg, Peter
Engineering · Mathematics · #Experimental Learning in Engineering #Rings, Modules, and Algebras #Advanced Data Processing Techniques
paper · pdf · doi:10.48550/arxiv.2505.07343
In [LWY23] the authors construct the reflective center of a module category M over a braided monoidal category B. The reflective center is by construction a braided module category over B. In the case where B is the category of modules over a finite dimensional quasitriangular Hopf algebra H, acting on the category of modules over a comodule algebra, they construct a comodule algebra, the reflective algebra, whose modules are precisely the reflective center. In the construction, Majid's transmutation of H plays a crucial rôle. This note centers on the transmuted H, seeking to ''explain'' its appearance through a generalization in which the acting category is no longer a module category, but admits an internal reconstructed Hopf algebra; the transmutation is a special case of this notion. As a result, in certain cases, the reflective center is simply the category of modules in M over that Hopf algebra in B.