Academy of Mathematics and Systems Science, CAS Colloquia & Seminars
Speaker:
Prof. Wolfgang Rump, University of Stuttgart,Germany
Inviter:
Title:
Orthogonality and right l-groups
Time & Venue:
2017.10.7 10:30-11:30 N205
Abstract:
Abstraction of orthogonality in a Hilbert space leads to the concept of orthomodular lattices (OML). If a greatest element is missing, we get a generalized OML in Janowitz’ sense (GOML). A GOML with reversed order is an L-algebra, a quantum structure which arises in topics like algebraic logic, quantum groups, lattice-ordered groups, braiding and Garside groups. We embed a GOML into an OML so that the GOML is recovered by a Jauch-Piron state. To any GOML we construct a universal group-valued measure into a right l-group, the structure group, which is a complete invariant of the GOML. For the OML of a finite dimensional Hilbert space, we identify the structure group with the paraunitary group.