Symmetry reduction of states. II: A non-commutative positivstellensatz for \(\mathbb{C} \mathbb{P}^n\)

DOI10.1016/j.laa.2022.05.011zbMath1501.46059arXiv2110.03437OpenAlexW3201714619WikidataQ113869458 ScholiaQ113869458MaRDI QIDQ2151578

Matthias Schötz, Philipp Schmitt

Publication date: 5 July 2022

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2110.03437

zbMATH Keywords

star productsymmetry reductionnon-commutative \(^\ast\)-algebranon-strict positivstellensatz

Mathematics Subject Classification ID

Real algebraic and real-analytic geometry (14P99) Quantizations, deformations for selfadjoint operator algebras (46L65)

Related Items (2)

On \(k\)-polycosymplectic Marsden-Weinstein reductions ⋮ Symmetry reduction of states. I

Cites Work

• Operator Positivstellensätze for noncommutative polynomials positive on matrix convex sets
• The \(K\)-moment problem for compact semi-algebraic sets
• Reduction of symplectic manifolds with symmetry
• A non-commutative real Nullstellensatz and Hilbert's 17th problem
• Real algebraic geometry for matrices over commutative rings
• A strict Positivstellensatz for the Weyl algebra
• ``Positive noncommutative polynomials are sums of squares.
• Phase space reduction for star-products: An explicit construction for \(\mathbb{C} P^ n\)
• Equivalence of order and algebraic properties in ordered \(^*\)-algebras
• A nuclear Weyl algebra
• Maximal quadratic modules on \(*\)-rings.
• Sums of squares on real algebraic surfaces
• A strict Positivstellensatz for enveloping algebras
• Noncommutative polynomials nonnegative on a variety intersect a convex set
• Algebras of fractions and strict Positivstellensätze for ∗-algebras
• Pure states, positive matrix polynomials and sums of hermitian squares
• Non-commutative Real Algebraic Geometry - Some Basic Concepts and First Ideas
• A non-commutative Positivstellensatz on isometries
• Sums of squares of regular functions on real algebraic varieties
• A noncommutative real nullstellensatz corresponds to a noncommutative real ideal: Algorithms
• An Invitation to Unbounded Representations of ∗-Algebras on Hilbert Space
• Subalgebras with converging star products in deformation quantization: An algebraic construction for C P n
• An elementary and constructive solution to Hilbert’s 17th Problem for matrices

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