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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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A classification theorem for Albert algebras
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by R. Parimala, R. Sridharan and Maneesh L. Thakur PDF
Trans. Amer. Math. Soc. 350 (1998), 1277-1284 Request permission

Abstract:

Let $k$ be a field whose characteristic is different from 2 and 3 and let $L/k$ be a quadratic extension. In this paper we prove that for a fixed, degree 3 central simple algebra $B$ over $L$ with an involution $\sigma$ of the second kind over $k$, the Jordan algebra $J(B,\sigma ,u,\mu )$, obtained through Tits’ second construction is determined up to isomorphism by the class of $(u,\mu )$ in $H^1(k,SU(B,\sigma ))$, thus settling a question raised by Petersson and Racine. As a consequence, we derive a “Skolem Noether” type theorem for Albert algebras. We also show that the cohomological invariants determine the isomorphism class of $J(B,\sigma ,u,\mu )$, if $(B,\sigma )$ is fixed.
References
Additional Information
  • R. Parimala
  • Affiliation: School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay-5, India
  • MR Author ID: 136195
  • Email: parimala@tifrvax.tifr.res.in
  • R. Sridharan
  • Affiliation: School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay-5, India
  • Email: sridhar@tifrvax.tifr.res.in
  • Maneesh L. Thakur
  • Affiliation: School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay-5, India
  • Email: maneesh@tifrvax.tifr.res.in
  • Received by editor(s): June 12, 1996
  • © Copyright 1998 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 350 (1998), 1277-1284
  • DOI: https://doi.org/10.1090/S0002-9947-98-02102-3
  • MathSciNet review: 1458310