Skip to main content
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 5
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Garibaldi, Skip and Guralnick, Robert M. 2016. Essential dimension of algebraic groups, including bad characteristic. Archiv der Mathematik, Vol. 107, Issue. 2, p. 101.

    Baek, Sanghoon 2015. Essential Dimension of Projective Orthogonal and Symplectic Groups of Small Degree. Communications in Algebra, Vol. 43, Issue. 2, p. 693.

    MacDonald, Mark L. 2011. Essential p-dimension of the normalizer of a maximal torus. Transformation Groups, Vol. 16, Issue. 4, p. 1143.

    MacDonald, Mark L. 2010. Cohomological invariants of Jordan algebras with frames. Journal of Algebra, Vol. 323, Issue. 6, p. 1665.

    Vial, Charles 2009. Operations in Milnor <mml:math altimg="si1.gif" display="inline" overflow="scroll" xmlns:xocs="" xmlns:xs="" xmlns:xsi="" xmlns="" xmlns:ja="" xmlns:mml="" xmlns:tb="" xmlns:sb="" xmlns:ce="" xmlns:xlink="" xmlns:cals=""><mml:mi>K</mml:mi></mml:math>-theory. Journal of Pure and Applied Algebra, Vol. 213, Issue. 7, p. 1325.

  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 145, Issue 2
  • September 2008, pp. 295-303

Cohomological invariants of odd degree Jordan algebras

  • MARK L. MacDONALD (a1)
  • DOI:
  • Published online: 01 September 2008

In this paper we determine all possible cohomological invariants of Aut(J)-torsors in Galois cohomology with mod 2 coefficients (characteristic of the base field not 2), for J a split central simple Jordan algebra of odd degree n ≥ 3. This has already been done for J of orthogonal and exceptional type, and we extend these results to unitary and symplectic type. We will use our results to compute the essential dimensions of some groups, for example we show that ed(PSp2n) = n + 1 for n odd.

Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[2]V. Chernousov and J.–P. Serre. Lower bounds for essential dimensions via orthogonal representations. J. Algebra 305 (2006), 10551070.

[8]D. Haile , M.-A. Knus , M. Rost and J.-P. Tignol . Algebras of odd degree with involution, trace forms and dihedral extensions. Israel J. Math. 96 (1996), 299340.

[12]N. Lemire . Essential dimension of algebraic groups and integral representations of Weyl groups. Transform. Groups 9 (2004), 337379.

[14]J. Milnor . Algebraic K-theory and quadratic forms. Invent. Math. 9 (1970), 318344.

[15]Z. Reichstein and B. Youssin . Essential dimensions of algebraic groups and a resolution theorem for G-varieties (with an appendix by János Kollár and Endre Szabó). Canad. J. Math. 52 (2000), 10181056.

[17]W. Scharlau . Quadratische Formen und Galois-Cohomologie. Invent. Math. 4 (1967), 238264.

[20]T. A. Springer and F. D. Veldkamp . Octonions, Jordan algebras and exceptional groups. Springer Monographs in Mathematics (Springer, 2000).

[21]A. R. Wadsworth and D. B. Shapiro . On multiples of round and Pfister forms. Math. Z. 157 (1977), 5362.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *