Hurwitz pairs and Clifford valued inner products

• Autorzy: Jan Cnops
• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1996
• Tom: 37
• Numer: 1
• Strony: 195-208

Daty

wydano

1996

Twórcy

autor

Jan Cnops

• Vakgroep Wiskundige Analyse, RUG, Galglaan 2, B-9000 Gent, Belgium

Bibliografia

• [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.
• [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.
• [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.
• [7] I.R. Porteous, Topological geometry, 2nd edition, Cambridge University Press, 1981.
• [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.
• [10] L.-S. Randriamihamison, Paires de Hurwitz pseudo-euclidiennes en signature quelconque, J. Phys. A: Math. Gen. 23 (1990), 2729-2749.