Isotopy and invariants of Albert algebras

  • Maneesh L. Thakur

    Tata Institute of Fundamental Research, Mumbai, India


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.

Cite this article

Maneesh L. Thakur, Isotopy and invariants of Albert algebras. Comment. Math. Helv. 74 (1999), no. 2, pp. 297–305

DOI 10.1007/S000140050090