Marcelo Aguiar:
Algebra based on real hyperplane arrangements
Abstract
We discuss an algebraic theory based on the geometry of real
hyperplane arrangements. We focus on the notion of Hopf monoid, for
which the key ingredient is furnished by the projection maps of Tits.
Geometric structures associated to arrangements afford examples of
Hopf monoids. We discuss examples arising from chambers,
subarrangements, and deformations of zonotopes. When specialized
to the braid arrangement, we recover Hopf algebraic structures on
combinatorial objects such as graphs, linear orders, and generalized
permutahedra studied in previous work with Federico Ardila.
This is joint work in progress with Swapneel Mahajan.