The Waring problem for matrix algebras, II

Brešar, Matej (author), Šemrl, Peter (author)

Let $f$ be a noncommutative polynomial of degree $m\ge 1$ over an algebraically closed field $F$ of characteristic $0$. If $n\ge m-1$ and $\alpha_1,\alpha_2,\alpha_3$ are nonzero elements from $F$ such that $\alpha_1+\alpha_2+\alpha_3=0$, then every trace zero $n\times n$ matrix over $F$ can be written as $\alpha_1 A_1+\alpha_2A_2+\alpha_3A_3$ for some $A_i$ in the image of $f$ in $M_n(F)$.

• Language: English
• Keywords: Waring problem, noncommutatative polynomials, matrix algebras
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2023
• Number of pages: Str. 1880-1889
• Numbering: Vol. 55, iss. 4
• PID: 20.500.12556/RUL-151894
• UDC: 512
• ISSN on article: 0024-6093
• DOI: 10.1112/blms.12825
• COBISS.SI-ID: 161733891
• Publication date in RUL: 25.10.2023

Record is a part of a journal

• Title: Bulletin of the London Mathematical Society
• Shortened title: Bull. Lond. Math. Soc.
• Publisher: Wiley, London Mathematical Society
• ISSN: 0024-6093
• COBISS.SI-ID: 25154560

Licences

• License: CC BY-NC-ND 4.0, Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
• Link: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Description: The most restrictive Creative Commons license. This only allows people to download and share the work for no commercial gain and for no other purposes.

Secondary language

• Language: Slovenian
• Keywords: Waringov problem, nekomutativni polinomi, matrične algebre

Projects

• Funder: ARRS - Slovenian Research Agency
• Project number: P1-0288
• Name: Algebra in njena uporaba

• Funder: ARRS - Slovenian Research Agency
• Project number: J1-2454
• Name: Izomorfizmi, izometrije in ohranjevalci