mdh.sePublications
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Real commutative division algebras
Uppsala Universitet.ORCID iD: 0000-0001-9177-9774
Uppsala Universitet.
2007 (English)In: Algebras and Representation Theory, ISSN 1386-923X, E-ISSN 1572-9079, Vol. 10, no 2, 179-196 p.Article in journal (Refereed) Published
Abstract [en]

The category of all two-dimensional real commutative division algebras is shown to split into two full subcategories. One of them is equivalent to the category of the natural action of the cyclic group of order 2 on the open right half plane ℝ>0 × ℝ. The other one is equivalent to the category of the natural action of the dihedral group of order 6 on the set of all ellipses in ℝ2 which are centered at the origin and have reciprocal axis lengths. Cross-sections for the orbit sets of these group actions are easily described. Together with ℝ they classify all real commutative division algebras up to isomorphism. Moreover we describe all morphisms between the objects in this classifying set, thus obtaining a complete picture of the category of all real commutative division algebras, up to equivalence. This supplements earlier contributions of Kantor and Solodovnikov, Hypercomplex Numbers: An Elementary Introduction to Algebras, Nauka, Moscow, 1973; Benkart et al., Hadronic J., 4: 497-529, 1981; and Althoen and Kugler, Amer. Math. Monthly, 90: 625-635, 1983, who achieved partial results on the classification of the realcommutative division algebras.

Place, publisher, year, edition, pages
2007. Vol. 10, no 2, 179-196 p.
National Category
Algebra and Logic
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-21727DOI: 10.1007/s10468-006-9040-3Scopus ID: 2-s2.0-33847308674OAI: oai:DiVA.org:mdh-21727DiVA: diva2:652507
Available from: 2013-09-30 Created: 2013-09-30 Last updated: 2014-12-08Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full textScopushttp://dx.doi.org/10.1007/s10468-006-9040-3

Search in DiVA

By author/editor
Darpö, Erik
In the same journal
Algebras and Representation Theory
Algebra and Logic

Search outside of DiVA

GoogleGoogle Scholar

Altmetric score

Total: 31 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf