Locality structures: vector spaces and lattices

03.07.2020, 11:00
Arbeitsgruppenseminar Analysis

Pierre Clavier (Uni Potsdam)

Given a locality (ie binary symmetric) relation T on a vector space V, it is in general difficult to decide if (V,T) is a locality vector space, that is to say if T respects the linear structure of V in some sense. With L. Guo, S. Paycha and B. Zhang, we have investigated the lattice structure of the set G(V) of linear subspaces of V. Recall that a lattice possesses two operations, the join and the meet, which are respectively the intersection and the sum for G(V). As a lattice, G(V) does not have nice properties such as distributativity and modularity, but it has their locality counterparts. We use this observation to build a one-to-one correspondence between a spacial class of locality relation on V and orthocomplement maps on G(V). This talk will focus on the presentation of concepts and not on technical proofs.

Meeting ID: 948 5995 9797
Password: 11235813