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
DOI: https://doi.org/10.1090/S0002-9939-1985-0776183-2
MathSciNet review: 776183
Full-text PDF

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] N. Jacobson, Structure and representations of Jordan algebras, Amer. Math. Soc., Colloq. Publ., vol. 39, Amer. Math. Soc., Providence, R. I., 1968. MR 0251099 (40:4330)
  • [3] -, Structure groups and Lie algebras of Jordan algebras of symmetric elements of associative algebras with involution, Adv. in Math. 20 (1976), 106-150. MR 0407103 (53:10886)
  • [4] T. Muir, A treatise on the theory of determinants, Dover, New York, 1960. MR 0114826 (22:5644)
  • [5] W. C. Waterhouse, Introduction to affine group schemes, Graduate Texts in Math., No. 66, Springer-Verlag, New York, 1979. MR 547117 (82e:14003)
  • [6] -, Automorphisms of $ \det ({X_{ij}})$: The group scheme approach, Adv. in Math. (to appear)
  • [7] -, Twisted forms of the determinant, J. Algebra 86 (1984), 60-75. MR 727368 (85c:11040)

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

DOI: https://doi.org/10.1090/S0002-9939-1985-0776183-2
Article copyright: © Copyright 1985 American Mathematical Society

American Mathematical Society