On the Möbius Algebra of Geometric Lattices

The Möbius algebra of a poset was introduced by Solomon and also studied by Greene in the special case of lattices. Let denote a geometric lattice. Our key idea is to consider all the characteristic polynomials of upper intervals in as components of one object, which is multiplicative. Now, by simple algebraic means we obtain new identities involving the characteristic polynomial and the Tutte polynomial of a geometric lattice.