Pairs of Clifford algebras of the Hurwitz type

Królikowski, Wiesław

Banach Center Publications, Tome 37 (1996), p. 327-330 / Harvested from The Polish Digital Mathematics Library

Résumé

For a given Hurwitz pair $[S (Q_{S}), V (Q_{V}), o]$ the existence of a bilinear mapping $⭑ : C (Q_{S}) \times C (Q_{V}) \to C (Q_{V})$ (where $C (Q_{S})$ and $C (Q_{V}$ ) denote the Clifford algebras of the quadratic forms $Q_{S}$ and $Q_{V}$ , respectively) generated by the Hurwitz multiplication “o” is proved and the counterpart of the Hurwitz condition on the Clifford algebra level is found. Moreover, a necessary and sufficient condition for "⭑" to be generated by the Hurwitz multiplication is shown.

Publié le : 1996-01-01

Zbl 0873.15021

EUDML-ID : urn:eudml:doc:208609

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     author = {Kr\'olikowski, Wies\l aw},
     title = {Pairs of Clifford algebras of the Hurwitz type},
     journal = {Banach Center Publications},
     volume = {37},
     year = {1996},
     pages = {327-330},
     zbl = {0873.15021},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv37i1p327bwm}
}

Królikowski, Wiesław. Pairs of Clifford algebras of the Hurwitz type. Banach Center Publications, Tome 37 (1996) pp. 327-330. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv37i1p327bwm/

Bibliographie

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[002] [3] J. Ławrynowicz and J. Rembieliński, On the composition of nondegenerate quadratic forms with an arbitrary index, Ann. Fac. Sci. Toulouse 10 (1989), 141-168. | Zbl 0701.15025

[003] [4] J. Ławrynowicz and J. Rembieliński, Pseudo-Euclidean Hurwitz pairs and the Kałuża-Klein theories, J. Phys. A Math. Gen. 20 (1987), 5831-5848. | Zbl 0654.15021