WFRF:(Svensson Christian)
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- Silvestrov, Sergei,1970-Lund University,Lunds universitet,Mälardalens högskola,Akademin för utbildning, kultur och kommunikation,Mathematics/Applied Mathematics,Matematik LTH,Matematikcentrum,Institutioner vid LTH,Lunds Tekniska Högskola,Mathematics (Faculty of Engineering),Centre for Mathematical Sciences,Departments at LTH,Faculty of Engineering, LTH (author)
Algebraic dependence of commuting elements in algebras
- Article/chapterEnglish2009
Publisher, publication year, extent ...
- Berlin, Heidelberg :Springer Berlin/Heidelberg,2009
- printrdacarrier
Numbers
- LIBRIS-ID:oai:DiVA.org:mdh-22080
- https://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-22080URI
- https://doi.org/10.1007/978-3-540-85332-9_23DOI
- https://lup.lub.lu.se/record/2799095URI
Supplementary language notes
- Language:English
- Summary in:English
Part of subdatabase
- SwePubSwePub
Classification
Notes
- 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.
Subject headings and genre
- NATURVETENSKAP Matematik Algebra och logik hsv//swe
- NATURAL SCIENCES Mathematics Algebra and Logic hsv//eng
- NATURVETENSKAP Matematik hsv//swe
- NATURAL SCIENCES Mathematics hsv//eng
- algebraic dependence
- algebraic curve
- commuting elements
- q-deformed Heisenberg algebras
- Mathematics/Applied Mathematics
- matematik/tillämpad matematik
Added entries (persons, corporate bodies, meetings, titles ...)
- Svensson, Christian (author)
- de Jeu, Marcel (author)
- Svensson, CharlotteLund University,Lunds universitet,Matematik LTH,Matematikcentrum,Institutioner vid LTH,Lunds Tekniska Högskola,Mathematics (Faculty of Engineering),Centre for Mathematical Sciences,Departments at LTH,Faculty of Engineering, LTH(Swepub:lu)math-csv (author)
- Mälardalens högskolaAkademin för utbildning, kultur och kommunikation (creator_code:org_t)
Related titles
- In:Generalized Lie theory in mathematics, physics and beyondBerlin, Heidelberg : Springer Berlin/Heidelberg, s. 265-28097835408533129783540853329
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