Clas Löfwall: The holonomy Lie algebra of matroids

We will recall the definition of the holonomy Lie algebra of a central hyperplane arrangement and we do the generalization to matroids. The notion of matroid will be defined and in particular the lattice of flats and still in particular the set of 2-flats which determine the holonomy Lie algebra. We will see that the set of 2-flats is the same as a set of subsets of a finite set such that two subsets have at most one element in common. We define the notion of a Lie algebra based on such a set of subsets and generalize the theory for holonomy Lie algebras of hyperplane arrangements developed in the paper by Papadima and Suciu.
The content of the talk will be very elementary.

References:

Stefan Papadima and Alexander I. Suciu, When does the associated graded Lie algebra of an arrangement group decompose?, Comment. Math. Helv. 81:4 (2006), 859–875.

Richard P. Stanley, An Introduction to Hyperplane Arrangements, Lecture 3, Matroids and geometric lattices, Lecture notes, IAS/Park City Mathematics Institute, 2004. 

Clas Löfwall, Decomposition theorems for a generalization of the holonomy Lie algebra of an arrangement, to appear in Communications in algebra

See also notes by Clas Löfwall here (pdf 208 kB) .