Isotopy and invariants of Albert algebras |
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Authors: | ML Thakur |
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Institution: | (1) School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai-5, India, e-mail: maneesh@math.tifr.res.in, IN |
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Abstract: | Let k be a field with characteristic different from 2 and 3. Let B be a central simple algebra of degree 3 over a quadratic extension K/k, which admits involutions of second kind. In this paper, we prove that if the Albert algebras and have same and invariants, then they are isotopic. We prove that for a given Albert algebra J, there exists an Albert algebra J' with , and . We conclude with a construction of Albert division algebras, which are pure second Tits' constructions.
Received: December 9, 1997. |
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Keywords: | , Jordan algebras, isotopy, Albert algebras, invariants, |
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