Tuesday, January 15, 14:00, 7.527
Carsten Dietzel, Structure groups of orthomodular lattices.
Boolean algebras represent the algebraic structure of classical
logic. In the same way, orthomodular lattices (OMLs) represent the algebraic
structure of quantum logic. In this talk, we will present a connection between
OMLs and right l-groups.
In the first part, we will explain how to construct for each OML X a structure
group G(X). This assignment gives an equivalence between the category of OMLs
and the category of right l-groups with a singular strong order unit. In the
second part, we will restrict to the case where X is the OML of subspaces of a
finite-dimensional vector space with an anisotropic, symmetric bilinear form.
In this case, G(X) admits an easy description in terms of matrix groups over