On the composition of nondegenerate quadratic forms with an arbitrary index
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 5, Volume 10 (1989) no. 1, pp. 141-168.
@article{AFST_1989_5_10_1_141_0,
     author = {{\L}awrynowicz, Julian and Rembieli\'nski, Jakub},
     title = {On the composition of nondegenerate quadratic forms with an arbitrary index},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {141--168},
     publisher = {Universit\'e Paul Sabatier},
     address = {Toulouse},
     volume = {Ser. 5, 10},
     number = {1},
     year = {1989},
     zbl = {0701.15025},
     language = {en},
     url = {http://archive.numdam.org/item/AFST_1989_5_10_1_141_0/}
}
TY  - JOUR
AU  - Ławrynowicz, Julian
AU  - Rembieliński, Jakub
TI  - On the composition of nondegenerate quadratic forms with an arbitrary index
JO  - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY  - 1989
SP  - 141
EP  - 168
VL  - 10
IS  - 1
PB  - Université Paul Sabatier
PP  - Toulouse
UR  - http://archive.numdam.org/item/AFST_1989_5_10_1_141_0/
LA  - en
ID  - AFST_1989_5_10_1_141_0
ER  - 
%0 Journal Article
%A Ławrynowicz, Julian
%A Rembieliński, Jakub
%T On the composition of nondegenerate quadratic forms with an arbitrary index
%J Annales de la Faculté des sciences de Toulouse : Mathématiques
%D 1989
%P 141-168
%V 10
%N 1
%I Université Paul Sabatier
%C Toulouse
%U http://archive.numdam.org/item/AFST_1989_5_10_1_141_0/
%G en
%F AFST_1989_5_10_1_141_0
Ławrynowicz, Julian; Rembieliński, Jakub. On the composition of nondegenerate quadratic forms with an arbitrary index. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 5, Volume 10 (1989) no. 1, pp. 141-168. http://archive.numdam.org/item/AFST_1989_5_10_1_141_0/

[1] Adem (J.). - Construction of some normed maps, Bol. Soc. Mat. Mexicana (2), t. 20, 1975, p. 59-75. | MR | Zbl

[2] .- On maximal sets of anticommuting matrices, Ibid. (2), t. 23, 1978, p. 61-67. | MR | Zbl

[3] Adem (J.).- On the Hurwitz problem over an arbitrary field I-II Ibid. (2), 25 1980, 29-51 and (2) , t. 26, 1986, p. 29-41. | MR | Zbl

[4] Cartan (E.).-The theory of spinors, transl. from French Paris : Hermann 1966. | MR | Zbl

[5] Chevalley (C.).-The algebraic theory of spinors. Columbia : Columbia Univ. Press 1954. | MR | Zbl

[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. | Numdam | MR | Zbl

[7] Construction d'algèbres de Lie graduées orthosymplectiques et conformosymplectiques minkowskiennes. - in : Seminar on deformations, Proceeding, Łódź-Warsaw 1982-84, Lectue Notes in Math. 1165, Berlin-Heidelberg-New York-Tokyo : Springer 1985, p. 52-83. | MR | Zbl

[8] Frohlich (A.), Mcevett (A.).-Forms over rings with involution, J. Algebra, t. 12, 1969, p. 79-104. | MR | Zbl

[9] Geramita (A.V.), Seberry (J.). - Orthogonal designs. Lecture Notes in Pure and Applied Math. 45, New York-Basel :Marcel Dekker 1979. | MR | Zbl

[10] Hestenes (D.).-A unified laguage for mathematics and physics, in : Clifford algebras and their applications in mathematical physics, Proceeding, Canterbury 1985 Dordrecht :Reidel 1986 p. 1-23. | MR | Zbl

[11] Hurwitz (A.).- Uber die Komposition der quadratischen Formen. Math. Ann. 88 1923, p. 1-25; reprinted in : A. Hurwitz, Mathematische Werke II. Basel Birkhäuser 1933 p. 641-666. | JFM

[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) 9 1985 p. 117-128. | MR | Zbl

[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" Cagliari 1985, to appear.

[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 : Springer 1985, p. 184-195. | MR | Zbl

[15] .- Supercomplex vector spaces and spontaneous symmetric breaking, in : Seminari di Geometria 1984, Bologna:Università di Bologna 1985, p. 131-154. | MR | Zbl

[16] .- Pseudo-euclidean Hurwitz pairs and generalized Fueter Equations. (a) Inst. Math. Polish Acad. Sci. Preprint p. 355, II + 10 1985 (b) In : Clifford algebras and their applications in mathematical physics, Proceedings, Canterbury 1985, Dordrecht : Reidel 1986 p.39-48. | MR | Zbl

[17] .- Pseudo-euclidean Hurwitz pairs and the Kaluza-Klein theories. J. Phys. A. Math. Gen., to appear. | MR

[18] .-Complete classification for pseudo-euclidean Hurwitz pairs including the symetry operations. Bull. Soc. Sci. Lettres Łódź 36, no. 29 (Série : Recherches sur les déformations 3, no. 39) 1986, p. 15.

[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] Lam, Kee Yuen, . - The algebraic theory of quadratic forms, Reading, MA : W.A. Benjamin, Inc. 1973.. | Zbl

[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. | MR | Zbl

[22] Porteous (I.R.).-Topological geometry, 2nd ed. Combridge : Cambridge Univ. Press 1981. | MR | Zbl

[23] Roman (P.). - Advanced quantum theory, Reading, MA : Addison-Wesley Publ. Co. 1965. | MR | Zbl

[24] Shapiro (D.B.).-Spaces of similarities I-II, J. Algebra 46 1977, p. 148-164 and p. 165-181. | MR | Zbl

[25] .- Spaces of similarities IV, Pac. J. Math, t. 69, 1977, p. 223-224. | MR | Zbl

[26] .- Hasse principle for the Hurwitz problem, J. reine angew. Math., t. 301, 1978, p. 179-190. | MR | Zbl

[27] .- Products of sums of squares, Expo. Math, t. 2, 1984, p. 235-261. | MR | Zbl

[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] .- A geometric approach to the Kadomtsev-Petviasvili system II. Ibid., to appear.

[30] Wadsworth (A.), Shapiro (D.B.).-Spaces of similarities III. J. Algebra t. 46 1977 p. 182-188. | MR | Zbl