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arXiv · 2412.13344

Weak Partial Representations

Felipe Castro·Glauber Quadros·Thaísa Tamusiunas
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Abstract

We introduce the notion of partial representation of a weak Hopf algebra. We present the universal algebra $H_{par}^w$, which factorizes these partial representations by algebra morphisms. Also, it is shown that $\Hp$ is isomorphic to a partial smash product, that it has the structure of a Hopf algebroid and also that it can be endowed with a quantum inverse semigroup structure. Moreover, it is shown that the algebra objects in the module category over $H_{par}^w$ correspond to symmetrical partial module algebras.

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Felipe Castro, Glauber Quadros, Thaísa Tamusiunas. 2024-12-17. Weak Partial Representations. https://arxiv.org/abs/2412.13344

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