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 ...

Let $Z/n$ denote the integers $\operatorname{mod} n$ and let $\mathscr{F}_n$ denote the finite Fourier transform on $L^2(Z/n)$. We let $\bigoplus\Sigma \mathscr{F}_n ...

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 ...