Jordan Algebras Over Algebraic Varieties

REFERENCES

• Achhammer , G. Albert Algebren Über Lokal Geringten Räumen. Ph.D. Thesis, FernUniversität Hagen, 1995. Preprint 262, Jordan Theory Preprint Archives: http://homepage.uibk.ac.at/
   Google Scholar
• Achhammer , G. ( 1994 ). The first Tits construction of Albert algebras over locally ringed spaces. In: Nonassociative Algebra and Its Applications (Oviedo, 1993). Math. Appl. 303. Dordrecht: Kluwer Acad. Publ., pp. 8–11 .
   Google Scholar
• Arason , J. , Elman , R. , Jacob , B. ( 1992 ). On indecomposable vector bundles . Comm. Alg. 20 : 1323 – 1351 .
   Web of Science ®Google Scholar
• Hartshorne , R. ( 1977 ). Algebraic Geometry . Graduate Texts in Mathematics , Vol. 52. Berlin–Heidelberg–New York : Springer-Verlag .
   Google Scholar
• Jacobson , N. ( 1968 ). Structure and Representations of Jordan Algebras. Amer. Math. Soc. Coll. Publ. 39. Providence, RI .
   Google Scholar
• Jacobson , N. ( 1981 ). Structure Theory of Jordan Algebras. University of Arkansas Lect. Notes in Math. (5), Fayetteville .
   Google Scholar
• Knus , M.-A. ( 1991 ). Quadratic and Hermitian Forms Over Rings . Berlin–Heidelberg–New York : Springer-Verlag .
   Google Scholar
• Knus , M. A. , Parimala , R. , Sridharan , R. ( 1981 ). Non-free projective modules over ℍ[x, y] and stable bundles over ℙ2(ℂ)* . Invent. Math. 65 : 13 – 27 .
   Web of Science ®Google Scholar
• Knus , M. A. , Merkurjev , A. , Rost , M. , Tignol , J.-P. ( 1998 ). The Book of Involutions. Vol. 44. AMS Coll. Publications .
   Google Scholar
• Loos , O. ( 2006 ). Generically algebraic Jordan algebras over commutative rings . J. Algebra 297 : 474 – 529 .
   Web of Science ®Google Scholar
• McCrimmon , K. ( 1969 ). The Freudenthal-Springer-Tits constructions of exceptional Jordan algebras . Trans. Amer. Math. Soc. 139 : 495 – 510 .
   Web of Science ®Google Scholar
• McCrimmon , K. ( 2004 ). A Taste of Jordan Algebras . Universitext , New York : Springer-Verlag .
   Google Scholar
• Milne , J. S. ( 1980 ). Étale Cohomology . Princeton : Princeton University Press .
   Google Scholar
• Parimala , R. , Suresh , V. , Thakur , M. L. ( 1997 ). Jordan algebras and F 4 bundles over the affine plane . J. Algebra 198 : 582 – 607 .
   Web of Science ®Google Scholar
• Parimala , R. , Sridharan , R. , Thakur , M. L. ( 1999 ). Tits' constructions of Jordan algebras and F 4 bundles on the plane . Compositio Mathematica 119 : 13 – 40 .
   Web of Science ®Google Scholar
• Petersson , H. P. ( 1993 ). Composition algebras over algebraic curves of genus zero . Trans. Amer. Math. Soc. 337 ( 1 ): 473 – 491 .
   Web of Science ®Google Scholar
• Petersson , H. P. (1999). The Albert algebra of generic matrices. Comm. Alg. 27(8):3703–3717.
   Web of Science ®Google Scholar
• Petersson , H. P. ( 2004 ). Structure theorems for Jordan algebras of degree three over fields of arbitrary characteristic . Comm. Algebra 32 ( 3 ): 1019 – 1049 .
   Web of Science ®Google Scholar
• Petersson , H. P. , Racine , M. L. ( 1986 ). Jordan algebras of degree 3 and the Tits process . J. Algebra 98 ( 1 ): 211 – 243 .
   Web of Science ®Google Scholar
• Petersson , H. P. , Racine , M. L. ( 1986 ). Classification of algebras arising from the Tits process . J. Algebra 98 ( 1 ): 244 – 279 .
   Web of Science ®Google Scholar
• Petersson , H. P. , Thakur , M. ( 2004 ). The étale Tits process of Jordan algebras revisited . J. Algebra 272 : 88 – 107 .
   Web of Science ®Google Scholar
• Pumplün , S. ( 1998 ). Quaternion algebras over elliptic curves . Comm. Algebra 26 ( 12 ): 4357 – 4373 .
   Web of Science ®Google Scholar
• Pumplün , S. ( 1998 ). The Witt ring of a Brauer–Severi variety . Manuscripta Math. 97 ( 1 ): 93 – 108 .
   Web of Science ®Google Scholar
• Pumplün , S. ( 2008 ). Albert algebras over curves of genus zero and one . J. Algebra 320 : 4178 – 4214 .
   Web of Science ®Google Scholar
• Scharlau , W. ( 1985 ). Quadratic and Hermitian Forms . Berlin–Heidelberg–New York : Springer-Verlag .
   Google Scholar
• Schafer , R. D. ( 1995 ). An Introduction to Nonassociative Algebras . New York : Dover Publ., Inc .
   Google Scholar
• Roby , N. ( 1963 ). Lois polynômes et lois formelles en théorie des modules . Ann. Sci. Ecole Norm. Sup. 3 ^e ser. t. 80 : 213 – 348 .
   Google Scholar
• Thakur , M. ( 1995 ). Cayley algebra bundles on revisited . Comm. Algebra 23 ( 13 ): 5119 – 5130 .
   Web of Science ®Google Scholar
• Communicated by I. Shestakov
   Google Scholar