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arXiv · 2509.08278

Fundamental theorem of transposed Poisson $(A,H)$-Hopf modules

Yan Ning·Daowei Lu·Dingguo Wang
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Abstract

Transposed Poisson algebra was introduced as a dual notion of the Poisson algebra by switching the roles played by the commutative associative operation and Lie operation in the Leibniz rule defining the Poisson algebra. Let $H$ be a Hopf algebra with a bijective antipode and $A$ an $H$-comodule transposed Poisson algebra. Assume that there exists an $H$-colinear map which is also an algebra map from $H$ to the transposed Poisson center of $A$. In this paper we generalize the fundamental theorem of $(A, H)$-Hopf modules to transposed Poisson $(A, H)$-Hopf modules and deduce relative projectivity in the category of transposed Poisson $(A, H)$-Hopf modules.

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Yan Ning, Daowei Lu, Dingguo Wang. 2025-09-10. Fundamental theorem of transposed Poisson $(A,H)$-Hopf modules. https://arxiv.org/abs/2509.08278

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