Poisson Modules over Hopf Poisson Order Algebras

Abstract: Hopf Poisson order (HPO) algebras were introduced and studied by Brown, Nazemian, and Zhang (preprint, 2024). We investigate the class of Poisson modules over HPO algebras and show that it forms a monoidal category. Moreover, we prove that the left homological integral of an HPO algebra $H$, denoted $ \int_H^l$, is a left Poisson module. It is also a right Poisson module if and only if $\int_H^l = \int_H^r $. References: - Hopf Poisson Order Algebras, K. Brown, Z. Nazemian, and J.J. Zhang, (preprint, 2024). - Homological Integrals of Hopf Algebras, D.-M. Lu, Q.-S. Wu, and J.J. Zhang, Trans. Amer. Math. Soc. 359 (2007), 4945–4975. - Category of Poisson Modules over HPO Algebras, Z. Nazemian, in progress.

Mathematics

Audience: researchers in the topic

European Quantum Algebra Lectures (EQuAL)

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