Noncommutative Real Algebraic Geometry Some Basic Concepts and First Ideas

By K. Schmuedgen. 2007

88 citations recorded by the source corpus.

We propose and discuss how basic notions (quadratic modules, positive elements, semialgebraic sets, Archimedean orderings) and results (Positivstellensatze) from real algebraic geometry can be generalized to noncommutative *-algebras. A version of Stengle's Positivstellensatz for n X n matrices of real polynomials is proved.

Subfields: Algebra and Number Theory, Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ef348c287fd6a6c222ee058da83734912adfcea3

How researchers see this paper

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In Algebra and Number Theory

1. J. William Helton
2. J. Cimprič
3. Christopher S. Nelson
4. Scott McCullough
5. Nathanial P. Brown Narutaka Ozawa
6. Gelu Popescu
7. Victor Vinnikov

In Applied Mathematics

1. J. William Helton
2. Scott McCullough
3. J. Cimprič
4. Christopher S. Nelson
5. Gelu Popescu
6. Victor Vinnikov
7. Nathanial P. Brown Narutaka Ozawa
8. Dmitry S. Kaliuzhnyi-Verbovetskyi

In Mathematical Physics

1. J. William Helton
2. J. Cimprič
3. Christopher S. Nelson
4. Scott McCullough
5. Victor Vinnikov
6. Gelu Popescu
7. Nathanial P. Brown Narutaka Ozawa
8. Dmitry S. Kaliuzhnyi-Verbovetskyi

Citations in the corpus

• A noncommutative real nullstellensatz corresponds to a noncommutative real ideal: Algorithms (2011, methodology): “Our approach to Noncommutative Real Algebraic Geometry is motivated by [4]; for alternative approaches see [12] and [7].”