# Pairs of Clifford algebras of the Hurwitz type

Banach Center Publications (1996)

- Volume: 37, Issue: 1, page 327-330
- ISSN: 0137-6934

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topKrólikowski, Wiesław. "Pairs of Clifford algebras of the Hurwitz type." Banach Center Publications 37.1 (1996): 327-330. <http://eudml.org/doc/208609>.

@article{Królikowski1996,

abstract = {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.},

author = {Królikowski, Wiesław},

journal = {Banach Center Publications},

keywords = {Hurwitz pairs; Clifford algebras; Clifford-Lipschitz group; composition algebra; quadratic space; spinor norm},

language = {eng},

number = {1},

pages = {327-330},

title = {Pairs of Clifford algebras of the Hurwitz type},

url = {http://eudml.org/doc/208609},

volume = {37},

year = {1996},

}

TY - JOUR

AU - Królikowski, Wiesław

TI - Pairs of Clifford algebras of the Hurwitz type

JO - Banach Center Publications

PY - 1996

VL - 37

IS - 1

SP - 327

EP - 330

AB - 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.

LA - eng

KW - Hurwitz pairs; Clifford algebras; Clifford-Lipschitz group; composition algebra; quadratic space; spinor norm

UR - http://eudml.org/doc/208609

ER -

## References

top- [1] W. Królikowski, On Fueter-Hurwitz regular mappings, Dissertationes Math. 353 (1996). Zbl0864.30038
- [2] J. Ławrynowicz and J. Rembieliński, Pseudo-Euclidean Hurwitz pairs and generalized Fueter equations, in: Clifford algebras and their applications in mathematical physics, Proc., Canterbury 1985, J. S. R. Chisholm and A. K. Common (eds.), Reidel, Dordrecht, 1986, 39-48.
- [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. Zbl0701.15025
- [4] J. Ławrynowicz and J. Rembieliński, Pseudo-Euclidean Hurwitz pairs and the Kałuża-Klein theories, J. Phys. A Math. Gen. 20 (1987), 5831-5848. Zbl0654.15021

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