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Algebraic dependence of commuting elements in algebras
Mälardalen University, School of Education, Culture and Communication. (Mathematics/Applied Mathematics)ORCID iD: 0000-0003-4554-6528
2009 (English)In: Generalized Lie theory in mathematics, physics and beyond / [ed] Silvestrov, S.D.; Paal, E.; Abramov, V.; Stolin, A., Springer Berlin/Heidelberg, 2009, 265-280 p.Chapter in book (Refereed)
Abstract [en]

The aim of this paper to draw attention to several aspects of the algebraic dependence in algebras. The article starts with discussions of the algebraic dependence problem in commutative algebras. Then the Burchnall—Chaundy construction for proving algebraic dependence and obtaining the corresponding algebraic curves for commuting differential operators in the Heisenberg algebra is reviewed. Next some old and new results on algebraic dependence of commuting q-difference operators and elements in q-deformed Heisenberg algebras are reviewed. The main ideas and essence of two proofs of this are reviewed and compared. One is the algorithmic dimension growth existence proof. The other is the recent proof extending the Burchnall–Chaundy approach from differential operators and the Heisenberg algebra to the q-deformed Heisenberg algebra, showing that the Burchnall—Chaundy eliminant construction indeed provides annihilating curves for commuting elements in the q-deformed Heisenberg algebras for q not a root of unity.

Place, publisher, year, edition, pages
Springer Berlin/Heidelberg, 2009. 265-280 p.
Keyword [en]
algebraic dependence, algebraic curve, commuting elements, q-deformed Heisenberg algebras
National Category
Algebra and Logic
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-22080DOI: 10.1007/978-3-540-85332-9_23ISBN: 978-3-540-85331-2 (print)ISBN: 978-3-540-85332-9 (print)OAI: oai:DiVA.org:mdh-22080DiVA: diva2:682316
Available from: 2013-12-27 Created: 2013-10-23 Last updated: 2014-01-21Bibliographically approved

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Publisher's full texthttp://dx.doi.org/10.1007/978-3-540-85332-9_23

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CiteExportLink to record
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Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
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Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
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  • asciidoc
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