A Note on Weak Post-Hopf Algebra Structures on the Sweedler Hopf Algebra

TL;DR

This paper introduces relaxed weak post-Hopf algebras by removing the unitary constraint, thoroughly characterizing their structures on the Sweedler Hopf algebra and revealing new algebraic configurations.

Contribution

It defines and characterizes a new class of relaxed weak post-Hopf algebras, expanding the understanding of algebraic structures related to the Sweedler Hopf algebra.

Findings

Identified a new class of relaxed weak post-Hopf algebraic structures

Provided a complete characterization of these structures on the Sweedler Hopf algebra

Demonstrated divergence from previously known weak post-Hopf algebra frameworks

Abstract

By omitting the unitary constraint from the definition of weak post-Hopf algebras, we introduce the concept of relaxed weak post-Hopf algebras, offering a thorough characterization of all feasible relaxed weak post-Hopf algebraic structures on the Sweedler Hopf algebra. This work reveals a distinct class of relaxed weak post-Hopf algebraic configurations, diverging from previously established weak post-Hopf algebraic frameworks.