From orthocomplementations to locality

Pierre Clavier; Li Guo; Sylvie Paycha; Bin Zhang

doi:10.3842/SIGMA.2021.027

From orthocomplementations to locality

Pierre Clavier
, Li Guo
, Sylvie Paycha
, Bin Zhang

Rutgers Newark, Math & Computer Science

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

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.

Original language	English (US)
Article number	027
Journal	Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Volume	17
DOIs	https://doi.org/10.3842/SIGMA.2021.027
State	Published - 2021

All Science Journal Classification (ASJC) codes

Analysis
Mathematical Physics
Geometry and Topology

Keywords

Lattice
Locality
Orthocomplementation
Poset
Renormalization

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10.3842/SIGMA.2021.027

Cite this

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title = "From orthocomplementations to locality",

abstract = "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.",

keywords = "Lattice, Locality, Orthocomplementation, Poset, Renormalization",

author = "Pierre Clavier and Li Guo and Sylvie Paycha and Bin Zhang",

year = "2021",

doi = "10.3842/SIGMA.2021.027",

language = "English (US)",

volume = "17",

journal = "Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)",

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T1 - From orthocomplementations to locality

AU - Clavier, Pierre

AU - Guo, Li

AU - Paycha, Sylvie

AU - Zhang, Bin

PY - 2021

Y1 - 2021

N2 - 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.

AB - 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.

KW - Lattice

KW - Locality

KW - Orthocomplementation

KW - Poset

KW - Renormalization

UR - https://www.scopus.com/pages/publications/85104310952

UR - https://www.scopus.com/pages/publications/85104310952#tab=citedBy

U2 - 10.3842/SIGMA.2021.027

DO - 10.3842/SIGMA.2021.027

M3 - Article

AN - SCOPUS:85104310952

SN - 1815-0659

VL - 17

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

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

M1 - 027

ER -

From orthocomplementations to locality

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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