# Hurwitz pairs and Clifford valued inner products

Banach Center Publications (1996)

- Volume: 37, Issue: 1, page 195-208
- ISSN: 0137-6934

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topCnops, Jan. "Hurwitz pairs and Clifford valued inner products." Banach Center Publications 37.1 (1996): 195-208. <http://eudml.org/doc/208597>.

@article{Cnops1996,

abstract = {After an overview of Hurwitz pairs we are showing how to actually construct them and discussing whether, for a given representation, all Hurwitz pairs of the same type are equivalent. Finally modules over a Clifford algebra are considered with compatible inner products; the results being then aplied to Hurwitz pairs.},

author = {Cnops, Jan},

journal = {Banach Center Publications},

keywords = {Hurwitz pairs; Clifford algebras; inner products; Clifford modules; sesquilinear forms; spinor spaces; functions of hypercomplex variables},

language = {eng},

number = {1},

pages = {195-208},

title = {Hurwitz pairs and Clifford valued inner products},

url = {http://eudml.org/doc/208597},

volume = {37},

year = {1996},

}

TY - JOUR

AU - Cnops, Jan

TI - Hurwitz pairs and Clifford valued inner products

JO - Banach Center Publications

PY - 1996

VL - 37

IS - 1

SP - 195

EP - 208

AB - After an overview of Hurwitz pairs we are showing how to actually construct them and discussing whether, for a given representation, all Hurwitz pairs of the same type are equivalent. Finally modules over a Clifford algebra are considered with compatible inner products; the results being then aplied to Hurwitz pairs.

LA - eng

KW - Hurwitz pairs; Clifford algebras; inner products; Clifford modules; sesquilinear forms; spinor spaces; functions of hypercomplex variables

UR - http://eudml.org/doc/208597

ER -

## References

top- [1] F. Brackx, R. Delanghe and F. Sommen, Clifford analysis, Pitman, London, 1982.
- [2] A. Hurwitz, Über die Komposition der quadratischen Formen von beliebig vielen Variablen, Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen Math. phys. Kl. (1898), 308-316, reprinted in: A. Hurwitz, Mathematische Werke II, Birkhäuser Verlag, Basel, 1933, 565-571.
- [3] A. Hurwitz, Über die Komposition der quadratischen Formen, Math. Ann. 88 (1923), 1-25, reprinted in: A. Hurwitz, Mathematische Werke II, Birkhäuser Verlag, Basel, 1933, 641-666.
- [4] J. Ławrynowicz and J. Rembieliński, Pseudo-euclidean Hurwitz pairs and generalized Fueter equations, in J. S. R. Chisholm and A. K. Common (eds): Clifford algebras and their applications in mathematical physics, D. Reidel Publ. Co. Dordrecht, 1986, 39-48. Zbl0597.15019
- [5] J. Ławrynowicz and J. Rembieliński, Complete classification for pseudo-euclidean Hurwitz pairs including symmetry applications, Bull Soc. Sci. Lettres Łódź 36, No. 29, 1986, 15 pp. Zbl0627.15012
- [6] P. Lounesto, Clifford algebras and spinors, in J. S. R. Chisholm and A. K. Common (eds): Clifford algebras and their applications in mathematical physics, D. Reidel Publ. Co. Dordrecht, 1986, 25-37. Zbl0596.15028
- [7] I.R. Porteous, Topological geometry, 2nd edition, Cambridge University Press, 1981. Zbl0446.15001
- [8] I.R. Porteous, Clifford algebra tables, in F. Brackx, R. Delanghe and H. Serras (eds.) Clifford algebras and their applications in mathematical physics, Kluwer, Dordrecht, 1993, 13-22.
- [9] E. Ramirez de Arellano, M. Shapiro and N. Vasilevski, Hurwitz pairs and Clifford algebra representations, in F. Brackx, R. Delanghe and H. Serras (eds.) Clifford algebras and their applications in mathematical physics, Kluwer, Dordrecht, 1993, 175-182. Zbl0832.15013
- [10] L.-S. Randriamihamison, Paires de Hurwitz pseudo-euclidiennes en signature quelconque, J. Phys. A: Math. Gen. 23 (1990), 2729-2749. Zbl0716.15018

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