Revisiting semigroups theory and its relations to geometry

Algebraic structures, such as semigroups, groups, algebras previously were considered as a branch of more abstract mathematics. With appearance of algebraic geometry, algebraic complex structures used throughout other areas of mathematics this started to change. With a recent increasing interest in hypergraph structures (see e.g. papers on this <a href="https://arxiv.org/abs/1806.05977" rel="noopener ugc nofollow" target="_blank">here</a>), these mathematical objects have developed various ways of describing higher-order interactions for complex systems. Here we are discuss ways to characterize on one hand the algebraic language which could unfold some of the properties of hypergraph structures, and on another hand, to deepen our understanding of the physical characteristics of hypergraphs, in particular, the irreducibility properties of higher order representations to the lower order ones. <a href="https://liubauer.medium.com/revisiting-semigroups-theory-and-its-relations-to-geometry-52e7fdb5cd65">Website</a>