Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 17 (2021), 027, 23 pages      arXiv:2007.03003
Contribution to the Special Issue on Noncommutative Manifolds and their Symmetries in honour of Giovanni Landi

From Orthocomplementations to Locality

Pierre Clavier a, Li Guo b, Sylvie Paycha a and Bin Zhang c
a) Institute of Mathematics, University of Potsdam, D-14476 Potsdam, Germany
b) Department of Mathematics and Computer Science, Rutgers University, Newark, NJ 07102, USA
c) School of Mathematics, Yangtze Center of Mathematics, Sichuan University, Chengdu, 610064, China

Received July 06, 2020, in final form March 02, 2021; Published online March 22, 2021

After some background on lattices, the locality framework introduced in earlier work by the authors is extended to cover posets and lattices. We then extend the correspondence between Euclidean structures on vector spaces and orthogonal complementations to a one-one correspondence between a class of locality structures and orthocomplementations on bounded lattices. This recasts in the context of renormalisation classical results in lattice theory.

Key words: locality; lattice; poset; orthocomplementation; renormalisation.

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