Weak Hopf algebra structures on hybrid numbers

TL;DR

This paper investigates the possible weak Hopf algebra structures on the set of hybrid numbers, including their source and target algebras and integrals, contributing to algebraic structure classification.

Contribution

It characterizes all weak Hopf algebra structures on hybrid numbers and computes associated source, target algebras, and integrals, which is a novel algebraic classification.

Findings

Identified all weak Hopf algebra structures on hybrid numbers

Computed source and target algebras for these structures

Analyzed integrals within the weak Hopf algebra context

Abstract

Let $\mathbb{K}$ be the set of hybrid numbers. This paper is to look for all the weak Hopf structures on $\mathbb{K}$. Once $\mathbb{K}$ is endowed with a structure of a weak Hopf algebra, we shall compute the source algebra and target algebra of $\mathbb{K}$. Also, we shall discuss the integrals in such weak Hopf algebra $\mathbb{K}$.