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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Symmetric determinants and Jordan norm similarities in characteristic $2$
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by William C. Waterhouse PDF
Proc. Amer. Math. Soc. 93 (1985), 583-589 Request permission

Abstract:

We first determine all linear changes of variable formally preserving symmetric determinants in characteristic 2; there are just slightly more of them than in other characteristics. We then restate this result in terms of affine group schemes. This allows us to apply descent theory, and thereby we prove a theorem on norm similarities of Jordan algebras in the one case left open by Jacobson.
References
    G. Frobenius, Über die Darstellung der endlichen Gruppen durch lineare Substitutionen, Berlin Sitzungsber, 1897, pp. 994-1015; Abhandlungen III, pp. 83-103.
  • Nathan Jacobson, Structure and representations of Jordan algebras, American Mathematical Society Colloquium Publications, Vol. XXXIX, American Mathematical Society, Providence, R.I., 1968. MR 0251099
  • N. Jacobson, Structure groups and Lie algebras of Jordan algebras of symmetric elements of associative algebras with involution, Advances in Math. 20 (1976), no. 2, 106–150. MR 407103, DOI 10.1016/0001-8708(76)90183-3
  • Thomas Muir, A treatise on the theory of determinants, Dover Publications, Inc., New York, 1960. Revised and enlarged by William H. Metzler. MR 0114826
  • William C. Waterhouse, Introduction to affine group schemes, Graduate Texts in Mathematics, vol. 66, Springer-Verlag, New York-Berlin, 1979. MR 547117
  • —, Automorphisms of $\det ({X_{ij}})$: The group scheme approach, Adv. in Math. (to appear)
  • William C. Waterhouse, Twisted forms of the determinant, J. Algebra 86 (1984), no. 1, 60–75. MR 727368, DOI 10.1016/0021-8693(84)90055-3
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Additional Information
  • © Copyright 1985 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 93 (1985), 583-589
  • MSC: Primary 14L15; Secondary 15A15, 17C20
  • DOI: https://doi.org/10.1090/S0002-9939-1985-0776183-2
  • MathSciNet review: 776183