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Session S16 - Quantum symmetries

Friday, July 16, 12:10 ~ 12:35 UTC-3

Filtered Frobenius algebras in monoidal categories

Chelsea Walton

Rice University, USA   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

We develop filtered-graded techniques for algebras in monoidal categories with the goal of establishing a categorical version of Bongale's 1967 result: A filtered deformation of a Frobenius algebra over a field is Frobenius as well. Towards the goal, we construct a monoidal associated graded functor, building on prior works of Ardizzoni-Menini, of Galatius et al., and of Gwillian-Pavlov. We then produce equivalent conditions for an algebra in a rigid monoidal category to be Frobenius in terms of the existence of categorical Frobenius form. These two results of independent interest are used to achieve our goal. We illustrate these results by defining braided Clifford algebras, which are filtered deformations of Bespalov et al.'s braided exterior algebras, and show that these are Frobenius algebras in braided, rigid monoidal categories.

Joint work with Harshit Yadav (Rice University).

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