Hurwitz pairs and Clifford valued inner products

Jan Cnops

Banach Center Publications (1996)

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

Abstract

top
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.

How to cite

top

Cnops, 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. [1] F. Brackx, R. Delanghe and F. Sommen, Clifford analysis, Pitman, London, 1982. 
  2. [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. [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. [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. [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. [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. [7] I.R. Porteous, Topological geometry, 2nd edition, Cambridge University Press, 1981. Zbl0446.15001
  8. [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. [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. [10] L.-S. Randriamihamison, Paires de Hurwitz pseudo-euclidiennes en signature quelconque, J. Phys. A: Math. Gen. 23 (1990), 2729-2749. Zbl0716.15018

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.