Isotopy and invariants of Albert algebras

  • Tata Institute of Fundamental Research, Colaba, Mumbai, India

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.

Cite this article

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

DOI 10.1007/S000140050090