BIRS Workshop Lecture Videos
On the Tits-Weiss conjecture on U-operators and the Kneser-Tits conjecture for some groups of type E_7 and E_8. Chernousov, Vladimir
Joint work with S. Alsaody and A. Pianzola. In the first part of the talk we remind the definition of an $R$-equivalence (introduced by Manin), state the Tits-Weiss conjecture on generation of structure groups of Albert algebras by $U$-operators and the Kneser-Tits conjecture for isotropic groups. In the second part of the talk we focus on computation of $R$-equivalence classes for groups of type $E_6$. As applications of our result we prove the Tits-Weiss conjecture and the Kneser-Tits conjecture for some isotropic groups of type $E_7$ and $E_8$.
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