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Valued Custom Skew Fields with Generalised PBW Property from Power Series Construction
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. (MAM)ORCID iD: 0000-0001-6140-180X
2016 (English)In: Engineering Mathematics II: Algebraic, Stochastic and Analysis Structures for Networks, Data Classification and Optimization / [ed] Sergei Silvestrov; Milica Rancic, Springer, 2016, 33-55 p.Chapter in book (Refereed)
Abstract [en]

This chapter describes a construction of associative algebras that, despite starting from a commutation relation that the user may customize quite considerably, still manages to produce algebras with a number of useful properties: they have a Poincaré–Birkhoff–Witt type basis, they are equipped with a norm (actually an ultranorm) that is trivial to compute for basis elements, they are topologically complete, and they satisfy their given commutation relation. In addition, parameters can be chosen so that the algebras will in fact turn out to be skew fields and the norms become valuations. The construction is basically that of a power series algebra with given commutation relation, stated to be effective enough that the other properties can be derived. What is worked out in detail here is the case of algebras with two generators, but only the analysis of the commutation relation is specific for that case.

Place, publisher, year, edition, pages
Springer, 2016. 33-55 p.
Series
Springer Proceedings in Mathematics and Statistics, ISSN 2194-1009 ; 179
Keyword [en]
associative algebras, Poincaré–Birkhoff–Witt basis, commutation relation, power series algebra
National Category
Algebra and Logic
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-33374DOI: 10.1007/978-3-319-42105-6_3Scopus ID: 2-s2.0-85012975630ISBN: 978-3-319-42104-9 (print)ISBN: 978-3-319-42105-6 (print)OAI: oai:DiVA.org:mdh-33374DiVA: diva2:1034019
Available from: 2016-10-11 Created: 2016-10-11 Last updated: 2017-03-02Bibliographically approved

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Publisher's full textScopushttp://www.springer.com/gp/book/9783319421049

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CiteExportLink to record
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Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
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  • nn-NB
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