Algebraic structures form the backbone of modern abstract algebra, encapsulating a wide range of systems such as groups, rings, fields, and modules, each characterised by distinct axiomatic properties ...

Algebraic structures such as operads, Lie algebras and higher A∞-algebras underpin many foundational aspects of modern mathematics. When combined with homotopy theory—the study of continuous ...

To begin to understand what mathematicians and physicists see in the abstract structures of symmetries, let’s start with a familiar shape. We are fond of saying things are symmetric, but what does ...

PNAS is the world's most-cited multidisciplinary scientific serial. It publishes high-impact research reports, commentaries, perspectives, reviews, colloquium papers, and actions of the Academy. In ...