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
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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