Biquaternion algebras and quartic extensions
Publications Mathématiques de l'IHÉS, Tome 77 (1993), pp. 63-102. 
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     author = {Lam, Tsit Yuen and Leep, David B. and Tignol, Jean-Pierre},
     title = {Biquaternion algebras and quartic extensions},
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     pages = {63--102},
     publisher = {Institut des Hautes \'Etudes Scientifiques},
     volume = {77},
     year = {1993},
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     zbl = {0801.11048},
     language = {en},
     url = {http://archive.numdam.org/item/PMIHES_1993__77__63_0/}
}
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Lam, Tsit Yuen; Leep, David B.; Tignol, Jean-Pierre. Biquaternion algebras and quartic extensions. Publications Mathématiques de l'IHÉS, Tome 77 (1993), pp. 63-102. http://archive.numdam.org/item/PMIHES_1993__77__63_0/

[A1] A. A. Albert, New results in the theory of normal division algebras, Trans. Amer. Math. Soc., 32 (1930), 171-195. | JFM | MR

[A2] A. A. Albert, On the Wedderburn norm condition for cyclic algebras, Bull. Amer. Math. Soc., 37 (1931), 301-312. | JFM | Zbl

[A3] A. A. Albert, A construction of non-cyclic normal division algebras, Bull. Amer. Math. Soc., 38 (1932), 449-456. | JFM | Zbl

[A4] A. A. Albert, Normal division algebras of degree four over an algebraic field, Trans. Amer. Math. Soc., 34 (1932), 363-372. | JFM | MR | Zbl

[A5] A. A. Albert, Structure of Algebras, Coll. Publ., Vol. 24, Amer. Math. Soc., Providence, R. I., 1961.

[AEJ] J. Kr. Arason, R. Elman and B. Jacob, Fields of cohomological 2-dimension 3, Math. Ann., 274 (1986), 649-657. | EuDML | MR | Zbl

[Ar1] J. Kr. Arason, Cohomologische invarianten quadratischer Formen, J. Algebra, 36 (1975), 448-491. | MR | Zbl

[Ar2] J. Kr. Arason, A proof of Merkurjev's theorem, Canadian Math. Soc. Conf. Proc., 4 (1984), 121-130. | MR | Zbl

[ART] S. A. Amitsur, L. H. Rowen and J.-P. Tignol, Division algebras of degree 4 and 8 with involution, Israel J. Math., 33 (1979), 133-148. | MR | Zbl

[DD] J. Diller and A. Dress, Zur Galoistheorie pythagoreischer Körper, Arch. Math., 16 (1965), 148-152. | MR | Zbl

[Dr] P. K. Draxl, Skew Fields, London Math. Soc. Lecture Note Series, Vol. 81, Cambridge University Press, 1983. | MR | Zbl

[EL1] R. Elman and T. Y. Lam, Pfister forms and K-theory of fields, J. Algebra, 23 (1972), 181-213. | MR | Zbl

[EL2] R. Elman and T. Y. Lam, Quadratic forms and the u-invariant, I, Math. Zeit., 131 (1973), 283-304. | MR | Zbl

[EL3] R. Elman and T. Y. Lam, Quadratic forms under algebraic extensions, Math. Ann., 219 (1976), 21-42. | MR | Zbl

[EL4] R. Elman and T. Y. Lam, On the quaternion symbol homomorphism gF : k2F → B(F), Proc. of Seattle Algebraic K-theory Conference, Lecture Notes in Math., Vol. 342, pp. 447-463, Berlin-Heidelberg-New York, Springer Verlag, 1972. | MR | Zbl

[ELP] R. Elman, T. Y. Lam and A. Prestel, On some Hasse principles over formally real fields, Math. Zeit., 134 (1973), 291-301. | MR | Zbl

[ELW1] R. Elman, T. Y. Lam and A. Wadsworth, Amenable fields and Pfister extensions, Proceedings of Conference in Quadratic Forms, Queen's Papers in Pure and Applied Mathematics, Vol. 46 (1976), 445-492. | MR | Zbl

[ELW2] R. Elman, T. Y. Lam and A. Wadsworth, Pfister ideals in Witt rings, Math. Ann., 245 (1979), 219-245. | MR | Zbl

[ELW3] R. Elman, T. Y. Lam and A. Wadsworth, Quadratic forms under multiquadratic extensions, Indagationes Math., 42 (1980), 131-145. | MR | Zbl

[Fr] A. Fröhlich, Orthogonal representations of Galois groups, Stiefel-Whitney classes and Hasse-Witt invariants, J. reine angew. Math., 360 (1985), 84-123. | Zbl

[J] B. Jacob, The Galois cohomology of Pythagorean fields, Invent. Math., 65 (1981), 97-113. | MR | Zbl

[Ja] N. Jacobson, Some applications of Jordan norms to involutorial associative algebras, Advances in Math., 48 (1983), 1-15. | MR | Zbl

[KLST] M.-A. Knus, T. Y. Lam, J.-P. Tignol and D. B. Shapiro, Discriminants of involutions on biquaternion algebras, preprint, November 1992. | Zbl

[KPS] M.-A. Knus, R. Parimala and R. Sridharan, A classification of rank 6 quadratic spaces via pfaffians, J. reine angew. Math., 398 (1989), 187-218. | MR | Zbl

[L1] T. Y. Lam, The Algebraic Theory of Quadratic Forms, W. A. Benjamin, Addison-Wesley, Reading, Mass., 1973. (Second Printing with Revisions, 1980). | Zbl

[L2] T. Y. Lam, Orderings, Valuations and Quadratic Forms, Conference Board of Mathematical Sciences Lecture Notes Series, Vol. 52, Amer. Math. Soc., Providence, R. I., 1983. | MR | Zbl

[L3] T. Y. Lam, Fields of u-invariant 6 after A. Merkurjev, in Ring Theory 1989 (in honor of S. A. Amitsur), ed. L. Rowen, Israel Mathematical Conference Proceedings, Vol. 1, pp. 12-30, Weizmann Science Press of Israel, 1989. | Zbl

[L4] T. Y. Lam, Ten Lectures on Quadratic Forms over Fields, Proc. Quadratic Form Conference (ed. G. Orzech), Queen's Papers on Pure and Applied Math., Vol. 46 (1977), pp. 1-102. | MR | Zbl

[LLT] T. Y. Lam, D. Leep and J.-P. Tignol, private notes.

[MSh] P. Mammone and D. Shapiro, The Albert quadratic form for an algebra of degree four, Proc. Amer. Math. Soc., 105 (1989), 525-530. | MR | Zbl

[Me] A. Merkurjev, On the norm residue symbol of degree 2, Dokl. Akad. Nauk SSSR, 261 (1981), 542-547. (English Translation) Soviet Math. Dokl., 24 (1981), 546-551. | Zbl

[MS1] A. Merkurjev and A. Suslin, K-cohomology of Severi-Brauer varieties and the norm residue homomorphism, Izv. Akad. Nauk SSSR, 66 (1982), 1011-1046. (English Translation) Math. USSR Izv., 21 (1983), 307-340. | Zbl

[MS2] A. S. Merkurjev and A. A. Suslin, The norm residue homomorphism of degree three, Izv. Akad. Nauk SSSR, Ser. Mat., 54 (1990). (English Translation) Math. USSR Izv., 36 (1991), 349-367. | Zbl

[Pf] A. Pfister, Quadratische Formen in beliebigen Körpern, Invent. Math., 1 (1966), 116-132. | MR | Zbl

[Pi] R. S. Pierce, Associative Algebras, Graduate Texts in Mathematics, Vol. 88, Berlin-Heidelberg-New York, Springer Verlag, 1982. | MR | Zbl

[Ra] M. L. Racine, A simple proof of a theorem of Albert, Proc. Amer. Math. Soc., 43 (1974), 487-488. | MR | Zbl

[Ro] M. Rost, Hilbert 90 for K3 for degree-two extensions, preprint, 1986.

[Sch] W. Scharlau, Quadratic and Hermitian Forms, Grundlehren der Math. Wiss., Vol. 270, Berlin-Heidelberg-New York, Springer Verlag, 1985. | MR | Zbl

[Se] J.-P. Serre, Lecture Notes, Harvard University, Fall, 1990.

[T1] J.-P. Tignol, Corps à involution neutralisés par une extension abélienne élémentaire, in Groupe de Brauer ; séminaire, Les Plans-sur-Bex, Suisse, 1980 (M. Kervaire and M. Ojanguren, eds), Lecture Notes in Math., Vol. 844, pp. 1-34, Berlin-Heidelberg-New York, Springer Verlag, 1981. | Zbl

[T2] J.-P. Tignol, On the corestriction of central simple algebras, Math. Zeit., 194 (1987), 267-274. | MR | Zbl

[Ta] T. Tamagawa, On quadratic forms and pfaffians, J. Fac. Sci. Tokyo (Sec. I), 24 (1977), 213-219. | MR | Zbl