Journal article
Geometry of free loci and factorization of noncommutative polynomials
Advances in mathematics (New York. 1965), v 331, pp 589-626
20 Jun 2018
Abstract
The free singularity locus of a noncommutative polynomial f is defined to be the sequence of hypersurfaces Zn(f)={X∈Mn(k)g:detf(X)=0}. The main theorem of this article shows that f is irreducible if and only if Zn(f) is eventually irreducible. A key step in the proof is an irreducibility result for linear pencils. Arising from this is a free singularity locus Nullstellensatz for noncommutative polynomials. Apart from consequences to factorization in a free algebra, the paper also discusses its applications to invariant subspaces in perturbation theory and linear matrix inequalities in real algebraic geometry.
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Details
- Title
- Geometry of free loci and factorization of noncommutative polynomials
- Creators
- J. William Helton - University of California San DiegoIgor Klep - University of AucklandJurij Volčič - Ben-Gurion University of the Negev
- Publication Details
- Advances in mathematics (New York. 1965), v 331, pp 589-626
- Publisher
- Elsevier
- Grant note
- University of Auckland (https://doi.org/10.13039/501100001537) DMS 1500835 / NSF (https://doi.org/10.13039/100000001) Mathematisches Forschungsinstitut Oberwolfach P1-0222; L1-6722; J1-8132 / Slovenian Research Agency (https://doi.org/10.13039/501100004329) Marsden Fund (https://doi.org/10.13039/501100009193)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000434747900015
- Scopus ID
- 2-s2.0-85046532613
- Other Identifier
- 991021861882504721
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- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Mathematics