Construction of Hopf algebroids

TL;DR

This paper introduces a method to construct Hopf algebroids with arbitrary base algebras using specific elements satisfying certain properties, expanding the theoretical framework of Hopf algebroids.

Contribution

It provides a new construction technique for Hopf algebroids over arbitrary base rings using elements with particular properties.

Findings

Constructed Hopf algebroids for any algebra L

Defined conditions on elements σ to ensure valid structures

Extended the class of known Hopf algebroids

Abstract

For arbitrary algebras $L$, we construct Hopf algebroids $A_\sigma$ with base rings $L$ by means of $\sigma^{ab}_{cd}\in L$ satisfying suitable properties.