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arXiv · 2405.12201

Quantum-symmetric equivalence is a graded Morita invariant

Hongdi Huang·Van C. Nguyen·Padmini Veerapen·Kent B. Vashaw·Xingting Wang
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Abstract

We show that if two $m$-homogeneous algebras have Morita equivalent graded module categories, then they are quantum-symmetrically equivalent, that is, there is a monoidal equivalence between the categories of comodules for their associated universal quantum groups (in the sense of Manin) which sends one algebra to the other. As a consequence, any Zhang twist of an $m$-homogeneous algebra is a 2-cocycle twist by some 2-cocycle from its Manin's universal quantum group.

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Hongdi Huang, Van C. Nguyen, Padmini Veerapen, Kent B. Vashaw, Xingting Wang. 2024-05-20. Quantum-symmetric equivalence is a graded Morita invariant. https://arxiv.org/abs/2405.12201

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