ALBERT ALGEBRAS AND THE TITS-WEISS CONJECTURE

Article Type

Research Article

Publication Title

Transactions of the American Mathematical Society

Abstract

We prove the Tits-Weiss conjecture for Albert division algebras over fields of arbitrary characteristic in the affirmative. The conjecture predicts that every norm similarity of an Albert division algebra is a product of a scalar homothety and U-operators. This conjecture is equivalent to the Kneser-Tits conjecture for simple, simply connected algebraic groups with Tits index E8782. We prove that a simple, simply connected algebraic group with Tits index E8782 or E7781, defined over a field of arbitrary characteristic, is R-trivial, in the sense of Manin, thereby proving the Kneser-Tits conjecture for such groups. The Tits-Weiss conjecture follows as a consequence.

First Page

6075

Last Page

6091

DOI

10.1090/tran/8744

Publication Date

9-1-2022

Comments

Open Access, Bronze, Green

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