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Liftings of dissident mapsPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2006 (English)In: Journal of Pure and Applied Algebra, ISSN 0022-4049, E-ISSN 1873-1376, Vol. 204, no 1, 133-154 p.Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

2006. Vol. 204, no 1, 133-154 p.
##### National Category

Algebra and Logic
##### Identifiers

URN: urn:nbn:se:uu:diva-22146DOI: 10.1016/j.jpaa.2005.04.005OAI: oai:DiVA.org:uu-22146DiVA: diva2:49919
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Available from: 2007-01-11 Created: 2007-01-11 Last updated: 2015-11-13Bibliographically approved

We study dissident maps ηη on R^{m}Rm for m∈{3,7}m∈{3,7} by investigating liftings Φ:R^{m}→R^{m}Φ:Rm→Rm of the selfbijection ηP:P(Rm)→P(Rm),ηP[v]=(η(v∧Rm))⊥ induced by ηη. Our main result (Theorem 2.4) asserts the existence and uniqueness, up to a non-zero scalar multiple, of a lifting ΦΦ whose component functions are homogeneous polynomials of degree dd, relatively prime and without non-trivial common zero. We prove that 1⩽d⩽m-21⩽d⩽m-2.

We achieve a complete description of all dissident maps of degree one and we solve their isomorphism problem (Theorems 4.8 and 4.13). As a consequence, we achieve a complete description of all real quadratic division algebras of degree one and we solve their isomorphism problem (Theorems 5.1 and 5.3). Moreover we present examples of eight-dimensional real quadratic division algebras of degree 3 and 5 (Proposition 6.3). This extends earlier results of Osborn [Trans. Amer. Math. Soc. 105 (1962) 202–221], Hefendehl [Geometriae Dedicata 9 (1980) 129–152], Hefendehl-Hebeker [Arch. Math. 40 (1983) 50–60], Cuenca Mira et al. [Lin. Alg. Appl. 290 (1999) 1–22], Dieterich [Proc. Amer. Math. Soc. 128 (2000) 3159–3166] and Dieterich and Lindberg [Colloq. Math. 97 (2003) 251–276] on the classification of real quadratic division algebras.

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