A standard form in (some) free fields: how to construct minimal linear representations

DOI10.1515/math-2020-0076zbMath1485.16016arXiv1803.10627OpenAlexW3108660119MaRDI QIDQ2053517

Konrad Schrempf

Publication date: 29 November 2021

Published in: Open Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1803.10627

zbMATH Keywords

free associative algebranon-commutative polynomialsadmissible linear systemleft greatest common divisorminimal linear representation

Mathematics Subject Classification ID

Infinite-dimensional and general division rings (16K40) Computational aspects of associative rings (general theory) (16Z05) Representation theory of associative rings and algebras (16G99) Matrix pencils (15A22) Associative rings of fractions and localizations (16S85)

Related Items (3)

Realizations of non‐commutative rational functions around a matrix centre, I: synthesis, minimal realizations and evaluation on stably finite algebras ⋮ Free (rational) derivation ⋮ Realizations of non-commutative rational functions around a matrix centre. II: The lost-abbey conditions

Cites Work

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• Constructive non-commutative rank computation is in deterministic polynomial time
• Geometry of free loci and factorization of noncommutative polynomials
• Applications of realizations (aka linearizations) to free probability
• Matrix coefficient realization theory of noncommutative rational functions
• Gröbner-Shirshov bases: from their inception to the present time.
• On the factorization of non-commutative polynomials (in free associative algebras)
• Rational identities and applications to algebra and geometry
• A Normal Form in Free Fields
• ON THE CONSTRUCTION OF THE FREE FIELD
• Linearizing the word problem in (some) free fields
• A Factorization Theory for some Free Fields
• Ideals, Varieties, and Algorithms
• Invariant Subspaces of Matrices with Applications

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