60
Views
3
CrossRef citations to date
0
Altmetric
Original Articles

An Embedding Theorem for Reduced Albert Algebras Over Arbitrary Fields

Pages 2062-2088 | Received 09 Jan 2014, Published online: 27 Feb 2015

REFERENCES

  • Alberca , P. , Loos , O. , Martín , C. ( 2005 ). Derivations and automorphisms of Jordan algebras in characteristic two . J. Algebra 285 ( 1 ): 146 – 181 .
  • Albert , A. A. , Jacobson , N. ( 1957 ). On reduced exceptional simple Jordan algebras . Ann. of Math. (2) 66 : 400 – 417 .
  • Anquela , J. , Cortés , T. , Petersson , H. P. ( 2014 ). Commuting U-operators in Jordan algebras . Trans. Amer. Math. Soc. 366 ( 1 ): 5877 – 5902 .
  • Borel , A. ( 1969 ). Linear Algebraic Groups . New York-Amsterdam : Notes taken by Hyman Bass. W. A. Benjamin, Inc .
  • Bruehne , P. ( 2000 ). Ordnungen und die Tits-Konstruktionen von Albert-Algebren. PhD thesis, Fernuniversität in Hagen .
  • Elman , R. , Karpenko , N. , Merkurjev , A. ( 2008 ). The Algebraic and Geometric Theory of Quadratic Forms, volume 56 of Coll. Publ . Providence , RI : Amer. Math. Soc .
  • Faulkner , J. R. ( 1970 ). Octonion planes defined by quadratic Jordan algebras. Memoirs of the American Mathematical Society. No. 104. Providence, R.I.: American Mathematical Society .
  • Garibaldi , S. , Petersson , H. P. (2011). Wild Pfister forms over Henselian fields, K-theory, and conic division algebras. J. Algebra 327:386–465.
  • Jacobson , N. ( 1968 ). Structure and Representations of Jordan Algebras . American Mathematical Society Colloquium Publications , Vol. XXXIX . Providence , R.I. : American Mathematical Society .
  • ——— . ( 1981 ). Structure Theory of Jordan Algebras , volume 5 of University of Arkansas Lecture Notes in Mathematics . Fayetteville , Ark : University of Arkansas .
  • Jacobson , N. , Katz , J. ( 1973 ). Generically algebraic quadratic Jordan algebras . Scripta Math. 29 ( 3–4 ): 215 – 227 . Collection of articles dedicated to the memory of Abraham Adrian Albert .
  • Jacobson , N. , McCrimmon , K. ( 1971 ). Quadratic Jordan algebras of quadratic forms with base points . J. Indian Math. Soc. (N.S.) 35 : 1 – 45 (1972) .
  • Knus , M.-A. , Merkurjev , A. , Rost , M. , Tignol , J.-P. ( 1998 ). The Book of Involutions, volume 44 of Amer. Math. Soc. Coll. Publ . Providence , RI : Amer. Math. Soc .
  • Loos , O. ( 1975 ). Jordan Pairs . Vol. 460 . Lecture Notes in Mathematics . Berlin : Springer-Verlag .
  • ——— . ( 2011 ). Algebras with scalar involution revisited . J. Pure Appl. Algebra 215 ( 12 ): 2805 – 2828 .
  • McCrimmon , K. ( 1969 ). The Freudenthal-Springer-Tits constructions of exceptional Jordan algebras . Trans. Amer. Math. Soc. 139 : 495 – 510 .
  • ——— . ( 1970 ). The Freudenthal-Springer-Tits constructions revisited . Trans. Amer. Math. Soc. 148 : 293 – 314 .
  • ——— . ( 1971 ). Homotopes of alternative algebras . Math. Ann. 191 : 253 – 262 .
  • ——— . ( 1985 ). Nonassociative algebras with scalar involution . Pacific J. Math. 116 ( 1 ): 85 – 109 .
  • Petersson , H. P. ( 2012 ). Albert algebras. http://www.fields.utoronto.ca/programs/scientific/11-12/exceptional/Alb.-alg.-Ottawa-2012-Vii-new.pdf.
  • Petersson , H. P. , Racine , M. L. ( 1986 ). Jordan algebras of degree 3 and the Tits process . J. Algebra 98 ( 1 ): 211 – 243 .
  • ——— . ( 1995 ). On the invariants mod 2 of Albert algebras . J. Algebra 174 ( 3 ): 1049 – 1072 .
  • Racine , M. L. ( 1972 ). A note on quadratic Jordan algebras of degree 3 . Trans. Amer. Math. Soc. 164 : 93 – 103 .
  • Roby , N. ( 1963 ). Lois polynomes et lois formelles en théorie des modules . Ann. Sci. École Norm. Sup. (3) 80 : 213 – 348 .
  • Schafer , R. D. ( 1995 ). An Introduction to Nonassociative Algebras . New York : Dover Publications Inc. Corrected reprint of the 1966 original .
  • Springer , T. A. , Veldkamp , F. D. ( 2000 ). octonions, Jordan algebras and exceptional groups . Springer Monographs in Mathematics . Berlin : Springer-Verlag .
  • Communicated by A. Elduque.

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.