Geodesic
Stably Cayley semisimple groups.
Documenta mathematica, Alexander S. Merkurjev's Sixtieth Birthday (2015), pp. 85-112.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

A linear algebraic group $G$ over a field $k$ is called a Cayley group if it admits a Cayley map, i.e., a $G$-equivariant birational isomorphism over $k$ between the group variety $G$ and its Lie algebra Lie$(G)$. A prototypical example is the classical "Cayley transform" for the special orthogonal group $\bold{SO}_n$ defined by Arthur Cayley in 1846. A linear algebraic group $G$ is called stably Cayley if $G \times S$ is Cayley for some split $k$-torus $S$. We classify stably Cayley semisimple groups over an arbitrary field $k$ of characteristic 0.
Classification : 20G15, 14L35, 14E05
Keywords: linear algebraic groups, Cayley groups, stably Cayley groups, character lattices, quasi-permutation lattices, Weil restriction of scalars 
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     title = {Stably {Cayley} semisimple groups.},
     journal = {Documenta mathematica},
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     year = {2015},
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Borovoi, Mikhail; Kunyavskii, Boris. Stably Cayley semisimple groups.. Documenta mathematica, Alexander S. Merkurjev's Sixtieth Birthday (2015), pp. 85-112. http://geodesic.mathdoc.fr/item/DOCMA_2015__S2__a19/