A note on non-commutative polytopes and polyhedra
Algebraic Geometry
2019-03-01 v3 Operator Algebras
Abstract
It is well-known that every polyhedral cone is finitely generated (i.e. polytopal), and vice versa. Surprisingly, the two notions differ almost always for non-commutative versions of such cones. This was obtained as a byproduct in an earlier paper. In this note we give a direct and constructive proof of the statement. Our proof also yields a surprising quantitative result: the difference of the two notions can always be seen at the first level of non-commutativity, i.e. for matrices of size , independent of dimension and complexity of the initial convex cone.
Keywords
Cite
@article{arxiv.1809.00476,
title = {A note on non-commutative polytopes and polyhedra},
author = {Beatrix Huber and Tim Netzer},
journal= {arXiv preprint arXiv:1809.00476},
year = {2019}
}