Year: 2025
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Ning, Yan, Lu, Daowei, Wang, Dingguo
Language: English
Topic: Advanced Topics in Algebra
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G4636551430, G8503811393
OpenAlex ID: W4417064441