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Algebraic dependenc...
Algebraic dependence of commuting elements in algebras
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- Silvestrov, Sergei, 1970- (författare)
- 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
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Svensson, Christian (författare)
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de Jeu, Marcel (författare)
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- Svensson, Charlotte (författare)
- Lund 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
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(creator_code:org_t)
- Berlin, Heidelberg : Springer Berlin/Heidelberg, 2009
- 2009
- Engelska.
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Ingår i: Generalized Lie theory in mathematics, physics and beyond. - Berlin, Heidelberg : Springer Berlin/Heidelberg. - 9783540853312 - 9783540853329 ; , s. 265-280
- Relaterad länk:
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http://dx.doi.org/10...
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http://arxiv.org/pdf...
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https://urn.kb.se/re...
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https://doi.org/10.1...
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https://lup.lub.lu.s...
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Abstract
Ämnesord
Stäng
- 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.
Ämnesord
- NATURVETENSKAP -- Matematik -- Algebra och logik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Algebra and Logic (hsv//eng)
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Nyckelord
- algebraic dependence
- algebraic curve
- commuting elements
- q-deformed Heisenberg algebras
- Mathematics/Applied Mathematics
- matematik/tillämpad matematik
Publikations- och innehållstyp
- ref (ämneskategori)
- kap (ämneskategori)
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