130
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

Hyperbolic Involutions and Quadratic Extensions

Pages 125-132 | Received 15 Sep 2009, Published online: 20 Jan 2011

REFERENCES

  • Bayer-Fluckiger , E. , Lenstra, Jr. , H. W. ( 1990 ). Forms in odd degree extensions and self-dual normal bases . Amer. J. Math. 112 : 359 – 373 .
  • Bayer-Fluckiger , E. , Shapiro , D. B. , Tignol , J.-P. ( 1993 ). Hyperbolic involutions . Math. Z. 214 : 461 – 476 .
  • Garibaldi , S. , Quéguiner-Mathieu , A. ( 2009 ). Pfister's theorem for orthogonal involutions of degree 12 . Proc. Am. Math. Soc. 137 : 1215 – 1222 .
  • Haile , D. E. , Morandi , P. J. ( 2001 ). Hyperbolicity of algebras with involution and connections with Clifford algebras . Comm. Algebra 29 : 5733 – 5753 .
  • Haile , D. E. , Tignol , J.-P. ( 1998 ). Algebras with involution that become hyperbolic under a given extension . J. Algebra 199 : 94 – 115 .
  • Knus , M.-A. , Merkurjev , A. , Rost , M. , Tignol , J.-P. 1998 . The Book of Involutions . American Mathematical Society Colloquium Publications, 44 . Providence , RI : American Mathematical Society .
  • Knus , M.-A. , Parimala , R. , Sridharan , R. ( 1991 ). On the discriminant of an involution . Bull. Soc. Math. Belg. Sér. A 43 : 89 – 98 .
  • Laghribi , A. ( 2001 ). Hyperbolicité de certaines involutions sur le corps des fonctions d'une quadrique . Indag. Math. (N. S.) 12 : 337 – 351 .
  • Lam , T. Y. ( 2005 ). Introduction to Quadratic forms Over Fields . Graduate Studies in Mathematics 67 . Providence , RI : American Mathematical Society (AMS) .
  • Lewis , D. W. ( 1985 ). Periodicity of Clifford algebras and exact octagons of Witt groups . Math. Proc. Cambridge Philos. Soc. 98 : 263 – 269 .
  • Lewis , D. W. , Unger , T. ( 2003 ). A local-global principle for algebras with involution and hermitian forms . Math. Z. 244 : 469 – 477 .
  • Mahmoudi , M. G. On hyperbolic Clifford algebras with involution. Accepted for publication in Algebra Colloq.
  • Quéguiner-Mathieu , A. , Tignol , J.-P. ( 2010 ). Algebras with involution that become hyperbolic over the function field of a conic . Israel J. Math. 180 : 317 – 344 .
  • Tignol , J.-P. ( 1996 ). A Cassels-Pfister theorem for involutions on central simple algebras . J. Algebra 181 : 857 – 875 .
  • Communicated by A. Prestel.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.