Magic(k)

Magic(k) is a mathematical concept involving objects called "abelian groups" (which are sets with an addition-like operation) combined with a special type of function called a "cocycle" that satisfies specific compatibility conditions across a structured system of groups. Think of it as a way to encode how certain symmetries or patterns behave consistently across different layers of mathematical structures. Magic(k) often appears in areas like algebra, topology, and number theory, where it helps analyze how local properties relate to global behavior, revealing deeper insights about the underlying structures.