Complex psd-minimal polytopes in dimensions two and three
-
Published:2022-11-10
Issue:
Volume:
Page:
-
ISSN:0219-4988
-
Container-title:Journal of Algebra and Its Applications
-
language:en
-
Short-container-title:J. Algebra Appl.
Author:
Bogart Tristram1,
Gouveia João2,
Torres Juan Camilo1
Affiliation:
1. Departamento de Matemáticas, Universidad de los Andes, Bogotá, Colombia
2. CMUC, Department of Mathematics, University of Coimbra, Coimbra, Portugal
Abstract
The extension complexity of a polytope measures its amenability to succinct representations via lifts. There are several versions of extension complexity, including linear, real semidefinite, and complex semidefinite. We focus on the last of these, for which the least is known, and in particular on understanding which polytopes are complex psd-minimal. We prove the existence of an obstruction to complex psd-minimality which is efficiently computable via lattice membership problems. Using this tool, we complete the classification of complex psd-minimal polygons (geometrically as well as combinatorially). In dimension three we exhibit several new examples of complex psd-minimal polytopes and apply our obstruction to rule out many others.
Funder
Faculty of Sciences of the Universidad de los
Portuguese government through FCT/MCTES
Publisher
World Scientific Pub Co Pte Ltd
Subject
Applied Mathematics,Algebra and Number Theory