ar X iv : m at h / 04 09 00 4 v 1 [ m at h . A G ] 1 S ep 2 00 4 CAYLEY GROUPS
نویسندگان
چکیده
The classical Cayley map, X → (In − X)(In + X) −1 , is a birational iso-morphism between the special orthogonal group SOn and its Lie algebra son, which is SOn-equivariant with respect to the conjugating and adjoint actions respectively. We ask whether or not maps with these properties can be constructed for other algebraic groups. We show that the answer is usually " no " , with a few exceptions. In particular, we show that a Cayley map for the group SLn exists if and only if n 3, answering an old question of Luna.
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تاریخ انتشار 2004