On the composition of nondegenerate quadratic forms with an arbitrary index

 Access to full text

 Full (PDF)

1. [1] Adem ( J.).—Construction of some normed maps, Bol. Soc. Mat. Mexicana (2), t. 20, 1975, p. 59-75. Zbl0498.17014MR466253
2. [2] - On maximal sets of anticommuting matrices, Ibid. (2), t. 23, 1978, p. 61-67. Zbl0447.15008MR579663
3. [3] Adem ( J.).—On the Hurwitz problem over an arbitrary field I-II Ibid. (2), 251980, 29-51 and (2) , t. 26, 1986, p. 29-41. Zbl0484.10013MR636968
4. [4] Cartan ( E.).—The theory of spinors, transl. from French Paris : Hermann1966. Zbl0147.40101MR208503
5. [5] Chevalley ( C.).—The algebraic theory of spinors. Columbia : Columbia Univ. Press1954. Zbl0057.25901MR60497
6. [6] Crumeyrolle ( A.).—Bilinéarité et géométrie affine attachées aux espaces de spineurs complexes, minkowskiens ou autres, Ann. Inst. Henri Poincaré, t. 34, 1981, p. 351-372. Zbl0454.53011MR612222
7. [7] Construction d'algèbres de Lie graduées orthosymplectiques et conformosymplectiques minkowskiennes. — in : Seminar on deformations, Proceeding, Łódź-Warsaw 1982-84, Lecture Notes in Math.1165, Berlin-Heidelberg-New York-TokyoSpringer : 1985, p. 52-83. Zbl0584.17010MR825748
8. [8] Frohlich ( A.), Mcevett ( A.).—Forms over rings with involution, J. Algebra, t. 12, 1969, p. 79-104. Zbl0256.15017MR274480
9. [9] Geramita ( A.V.), Seberry ( J.). — Orthogonal designs. Lecture Notes in Pure and Applied Math.45, New York-Basel : Marcel Dekker1979. Zbl0411.05023MR534614
10. [10] Hestenes ( D.).—A unified laguage for mathematics and physics, in : Clifford algebras and their applications in mathematical physics, Proceeding, Canterbury 1985Dordrecht : Reidel1986 p. 1-23. Zbl0596.15027MR863423
11. [11] Hurwitz ( A.).— Uber die Komposition der quadratischen Formen. Math. Ann.881923, p. 1-25; reprinted in : A. Hurwitz, Mathematische Werke II. BaselBirkhäuser1933 p. 641-666. JFM48.1164.03
12. [12] Kalina ( J.), Ławrynowicz ( J.), Suzuki ( O.).— A field equation defined by a Hurwitz pair, in Proc. of the 13th Winter School on Abstract Analysis, Srni 1985. Suppl. Rend. Circ. Mat. Palermo (2) 91985 p. 117-128. Zbl0613.35066MR853134
13. [13] .- Partial differential equations connected with some Clifford structures and the related quasiconformal mappings, in Proc. Conf. "Metodi di Analisi Reale nelle Equaziono alle Derivate Parziali" Cagliari1985, to appear. 
14. [14] Ławrynowicz ( J.), Rembielinski ( J.).— Hurwitz pairs equipped with complex structures, in : Seminar on deformations, Proceedings, Łódź-Warsaw—1982—84-Lecture Notes in Math.1165, Berlin-Heidelberg-New-York-Tokyo : Springer1985, p. 184-195. Zbl0591.15019MR825754
15. [15] .- Supercomplex vector spaces and spontaneous symmetric breaking, in : Seminari di Geometria 1984, Bologna : Università di Bologna1985, p. 131-154. Zbl0605.30050MR866154
16. [16] .— Pseudo-euclidean Hurwitz pairs and generalized Fueter Equations. (a) Inst. Math. Polish Acad. Sci. Preprint p. 355, II + 101985 (b) In : Clifford algebras and their applications in mathematical physics, Proceedings, Canterbury 1985, Dordrecht : Reidel1986 p.39-48. Zbl0597.15019MR863425
17. [17] .— Pseudo-euclidean Hurwitz pairs and the Kaluza-Klein theories. J. Phys. A. Math. Gen., to appear. Zbl0654.15021MR939891
18. [18] .— Complete classification for pseudo-euclidean Hurwitz pairs including the symetry operations. Bull. Soc. Sci. Lettres Łódź36, no. 29 (Série : Recherches sur les déformations3, no. 39) 1986, p. 15. Zbl0627.15012
19. [19] RAMIREZ DE ARELLANO ( E.) Wene ( G.P.).— The correspondance between type-changing transformations of pseudo-euclidean Hurwitz pairs and Clifford algebras in preparation. 
20. [20] Lam, Kee Yuen. — The algebraic theory of quadratic forms, Reading, MA : W.A. Benjamin, Inc.1973.. Zbl0259.10019
21. [21] Lee ( H.C.).—Sur le théorème de Hurwitz-Radon pour la composition des formes quadratique, Comment. Math. Helv., t. 21, 1948, p. 261-269. Zbl0030.29203MR26637
22. [22] Porteous ( I.R.). - Topological geometry, 2nd ed. Combridge : Cambridge Univ. Press1981. Zbl0446.15001MR606198
23. [23] Roman ( P.). - Advanced quantum theory, Reading, MA : Addison-Wesley Publ. Co.1965. Zbl0127.18603MR192757
24. [24] Shapiro ( D.B.).—Spaces of similarities I-II, J. Algebra461977, p. 148-164 and p. 165-181. Zbl0358.15024MR453636
25. [25] .— Spaces of similarities IV, Pac. J. Math, t. 69, 1977, p. 223-224. Zbl0326.15015MR476634
26. [26] .- Hasse principle for the Hurwitz problem, J. reine angew. Math., t. 301, 1978, p. 179-190. Zbl0376.10018MR506082
27. [27] .- Products of sums of squares, Expo. Math, t. 2, 1984, p. 235-261. Zbl0541.10025MR783137
28. [28] Suzuki ( O.), Ławrynowicz ( J.), Kalina ( J.), Kanemaki ( S.).— A geometric approach to the Kadomtsev-Petviasvili system I, Proc. Inst. Nat. Sci. Coll. Hum. Sci. Nihon Univ, t. 21, 1986, p. 11-34. 
29. [29] .- A geometric approach to the Kadomtsev-Petviasvili system II. Ibid., to appear. 
30. [30] Wadsworth ( A.), Shapiro ( D.B.). - Spaces of similarities III. J. Algebra t. 461977 p. 182-188. Zbl0358.15026MR453638