What is a hoop group?

In mathematics, specifically in the context of algebra and representation theory, a hoop group is a type of algebraic structure that arises from the study of certain topological or geometric spaces. It is often related to the concept of "hoops," which are sets equipped with a binary operation that satisfies specific axioms. These groups can be used to model various phenomena in fields like algebraic topology and combinatorial algebra. The precise definition and properties can vary depending on the context in which the term is used.