Pairs of Clifford algebras of the Hurwitz type

Volume 37 / 1996

Wiesław Królikowski Banach Center Publications 37 (1996), 327-330 DOI: 10.4064/-37-1-327-330


For a given Hurwitz pair $[S(Q_{S}),V(Q_{V}),o]$ the existence of a bilinear mapping $⭑: C(Q_{S}) × C(Q_{V}) → C(Q_{V})$ (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.


  • Wiesław Królikowski

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