The generalized Radon-Hurwitz numbers

Marc A. Berger; Shmuel Friedland

Compositio Mathematica (1986)

  • Volume: 59, Issue: 1, page 113-146
  • ISSN: 0010-437X

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Berger, Marc A., and Friedland, Shmuel. "The generalized Radon-Hurwitz numbers." Compositio Mathematica 59.1 (1986): 113-146. <http://eudml.org/doc/89776>.

@article{Berger1986,
author = {Berger, Marc A., Friedland, Shmuel},
journal = {Compositio Mathematica},
keywords = {Radon-Hurwitz matrices; generalized Radon-Hurwitz number; normed bilinear map; tables; periodicity},
language = {eng},
number = {1},
pages = {113-146},
publisher = {Martinus Nijhoff Publishers},
title = {The generalized Radon-Hurwitz numbers},
url = {http://eudml.org/doc/89776},
volume = {59},
year = {1986},
}

TY - JOUR
AU - Berger, Marc A.
AU - Friedland, Shmuel
TI - The generalized Radon-Hurwitz numbers
JO - Compositio Mathematica
PY - 1986
PB - Martinus Nijhoff Publishers
VL - 59
IS - 1
SP - 113
EP - 146
LA - eng
KW - Radon-Hurwitz matrices; generalized Radon-Hurwitz number; normed bilinear map; tables; periodicity
UR - http://eudml.org/doc/89776
ER -

References

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  1. [1] J.F. Adams: Vector fields on spheres, Ann. Math.75 (1962) 603-632. Zbl0112.38102MR139178
  2. [2] J.F. Adams: Geometric dimension of bundles over RPn, Proc. of the International Conference on Prospects of Math., Research Institute for Mathematical Sciences, Kyoto Univ., April 1973, 1-17. Zbl0336.55021MR482761
  3. [3] J. Adem: Construction of some normed maps, Bol. Soc. Mat. Mexicana23 (1978) 61-67. Zbl0498.17014MR466253
  4. [4] J. Adem: Algebra lineal, campos vectoriales e inmersiones, IIIELAM, IMPA, Rio de Janeiro, 1978. 
  5. [5] J. Adem: On maximal sets of anticommuting matrices, Bol. Soc. Mat. Mexicana23 (1978) 61-67. Zbl0447.15008MR579663
  6. [6] J. Adem: On the Hurwitz problem over an arbitrary field I, Bol. Soc. Mat. Mexicana25 (1980) 28-51. Zbl0484.10013MR636968
  7. [7] J. Adem: On the Hurwitz problem over an arbitrary field II, Bol. Soc. Mat. Mexicana26 (1981) 29-41. Zbl0514.10016MR742013
  8. [8] F. Behrend: Über Systems reeler algebraischer Gleichungen, Comp. Math.7 (1939-40) 1-19. Zbl0021.29301MR226JFM65.0051.01
  9. [9] A.J. Berrick: Projective space immersions, bilinear maps and stable homotopy groups of spheres, Lecture Notes in Mathematics, Vol. 168, Springer, Berlin, 1970, 11-24. Zbl0432.57009MR585649
  10. [10] W.K. Clifford: On the classification of geometric algebras, published as paper XLIII in Mathematical Papers (ed. R. Tucker), Macmillan, London, 1882. 
  11. [11] B. Eckmann: Gruppentheoretische Beweis des Satzes von Hurwitz-Radon über die Komposition quadratischer Formen, Comment. Math. Helvet.15 (1942-43) 358-366. Zbl0028.10402MR8592
  12. [12] S. Friedland: Simultaneous similarity of matrices, Adv. Math.50 (1983) 189-265. Zbl0532.15009MR724475
  13. [13] S. Friedland, J.W. Robin and J.H. Sylvester: On the crossing rule, Comm. Pure Appl. Math. (1984) 19-37. Zbl0507.15009MR728265
  14. [14] A.V. Geramita and J. Seberry: Orthogonal Designs, Marcel Dekker, New York, 1979. Zbl0411.05023MR534614
  15. [15] S. Gitler and K.Y. Lam: The generalized vector field problem and bilinear maps, Bol. Soc. Mat. Mexicana14 (1969) 65-69. Zbl0222.55026
  16. [16] H. Hopf: Ein topologischer Beitrag zur reelen Algebra, Comment. Math. Helvet.13 (1940-41) 219-239. Zbl0024.36002MR4785JFM67.0737.03
  17. [17] A. Hurwitz: Über die Komposition der quadratische Formen von beliebig vielen variabeln, Nachr. K. Gessellsch. Gottingen M. Ph. K1. (1898) 309-316. JFM29.0177.01
  18. [18] A. Hurwitz: Über die Komposition der quadratischen Formen, Math. Ann.88 (1923) 1-25. MR1512117JFM48.1164.03
  19. [19] K.Y. Lam: Non-singular bilinear forms and vector bundles over Pn, Ph.D. dissertation, Princeton University, 1966. 
  20. [20] K.Y. Lam: Construction of nonsingular bilinear maps, Topology6 (1967) 423-426. Zbl0149.40902MR217805
  21. [21] K.Y. Lam: Topological methods for studying the composition of quadratic forms, Canad. Math. Soc. Conf. Proc.4 (1984) 173-192. Zbl0559.10013MR776453
  22. [22] K.Y. Lam: Some new results on composition of quadratic forms, Invent. Math., 79 (1985) 467-474. Zbl0559.10014MR782229
  23. [23] J. Radon: Lineare scharen orthogonalen matrizen, Abh. Math. Sem. Univ. Hamburg1 (1922) 2-14. Zbl48.0092.06JFM48.0092.06
  24. [24] D.B. Shapiro: Products of sums of squares, Expos. Math., 2 (1984) 235-261. Zbl0541.10025MR783137
  25. [25] E. Stiefel: Richtungsfelder und Fernparallelismus in n-dimensionalen Mannigfaltigkeiten, Comment. Math. Helvet.8 (1936) 305-353. Zbl0014.41601MR1509530JFM62.0662.02

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