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Albert algebras and the Tits-Weiss conjecture by Thakur, Maneesh is a scholarly article available to read on EtoBox.

What is Albert algebras and the Tits-Weiss conjecture about?

We prove the Tits-Weiss conjecture for Albert division algebras over fields of arbitrary characteristics 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 $E^{78}_{8,2}$. We prove that a simple, simply connected algebraic group with Tits index $E_{8,2}^{78}$ or $E_{7,1}^{78}$, 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.

Author

Thakur, Maneesh

Published

2019

Language

EN