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A classification theorem for Albert algebras


Authors: R. Parimala, R. Sridharan and Maneesh L. Thakur
Journal: Trans. Amer. Math. Soc. 350 (1998), 1277-1284
DOI: https://doi.org/10.1090/S0002-9947-98-02102-3
MathSciNet review: 1458310
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Abstract | References | Additional Information

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.


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Additional Information

R. Parimala
Affiliation: School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay-5, India
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

DOI: https://doi.org/10.1090/S0002-9947-98-02102-3
Received by editor(s): June 12, 1996
Article copyright: © Copyright 1998 American Mathematical Society

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