Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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



Symmetric determinants and Jordan norm similarities in characteristic $ 2$

Author: William C. Waterhouse
Journal: Proc. Amer. Math. Soc. 93 (1985), 583-589
MSC: Primary 14L15; Secondary 15A15, 17C20
MathSciNet review: 776183
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] G. Frobenius, Über die Darstellung der endlichen Gruppen durch lineare Substitutionen, Berlin Sitzungsber, 1897, pp. 994-1015; Abhandlungen III, pp. 83-103.
  • [2] Nathan Jacobson, Structure and representations of Jordan algebras, American Mathematical Society Colloquium Publications, Vol. XXXIX, American Mathematical Society, Providence, R.I., 1968. MR 0251099
  • [3] 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 0407103
  • [4] Thomas Muir, A treatise on the theory of determinants, Revised and enlarged by William H. Metzler, Dover Publications, Inc., New York, 1960. MR 0114826
  • [5] William C. Waterhouse, Introduction to affine group schemes, Graduate Texts in Mathematics, vol. 66, Springer-Verlag, New York-Berlin, 1979. MR 547117
  • [6] -, Automorphisms of $ \det ({X_{ij}})$: The group scheme approach, Adv. in Math. (to appear)
  • [7] William C. Waterhouse, Twisted forms of the determinant, J. Algebra 86 (1984), no. 1, 60–75. MR 727368, 10.1016/0021-8693(84)90055-3

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 14L15, 15A15, 17C20

Retrieve articles in all journals with MSC: 14L15, 15A15, 17C20

Additional Information

Article copyright: © Copyright 1985 American Mathematical Society