English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this work we are interested in the general problem of the determination ofthe normed division algebras. Our fundamental results are obtained in theparticular subclass of those 8-dimensional quadratic flexible real divisionalgebras.  We give a new process which generalizes that of Cayley-Dickson and whichallows the obtaining of a new family of eight-dimensional quadratic flexiblereal division algebras. We give examples of 8-dimensional quadratic flexiblereal division algebras which cannot be obtained by this first process ofduplication and by means of a second process, which consists in making anappropriate deformation of the product of the octonion algebra, we determinethese last ones and we resolve the isomorphism problem. Among theeight-dimensional quadratic flexible real division algebras, we study thosewhich possess a nontrivial derivation by mean of the generalized Cayley-Dicksonprocess. We also give examples where the group of automorphisms is trivial, andcharacterize the algebras whose group of automorphisms is not trivial. Thisbrings to light the unlimitedness of this subclass of algebras.

Algebres non associatives normees de division. Classification des algebres reelles de Jordan non commutatives de division lineaire de dimension 8