Outer automorphisms of adjoint groups of type D and nonrational adjoint groups of outer type A
(2019) Transactions of the American mathematical society — Vol. 372, n° 4, p. 2613-2630 (2019)
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- Authors
Tignol, Jean-Pierre 
- Abstract
- For a classical group G of type Dn over a field k of characteristic different from 2, we show the existence of a finitely generated regular extension of k over which G admits outer automorphisms. Using this result and a construction of groups of type A from groups of type D, we construct new examples of groups of type 2An with n ≡ 3 mod 4 and the first examples of type 2An with n ≡ 1 mod 4 (n ≥ 5) that are not R-trivial, hence not rational (nor stably rational).
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Citations
Barry, D., & Tignol, J.-P. (2019). Outer automorphisms of adjoint groups of type D and nonrational adjoint groups of outer type A. Transactions of the American mathematical society, 372(4), 2613-2630. https://doi.org/10.1090/tran/7647 (Original work published 2019)