A result due to Joyal, Klyachko, and Stanley relates free Lie algebras to partition lattices. We will discuss the precise relationship and interpret the result in terms of the braid hyperplane arrangement. We will then extend this result to arbitrary (finite, real, and central) hyperplane arrangements, and do the same with several additional aspects of classical Hopf-Lie theory. The Tits monoid of an arrangement, and the notion of lune, play central roles in the discussion.
This is joint work with Swapneel Mahajan.
This video was produced by the Universidade de São Paulo, as part of the LieJor Online Seminar: Algebras, Representations, and Applications.
