Cayley groups
Cayley groups
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凯莱集团
DOI：
10.1090/s0894-0347-06-00522-4
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发表时间：
2004
影响因子：
1.4
通讯作者：
Z. Reichstein
中科院分区：
文献类型：
--
作者：
N. Lemire;V. Popov;Z. Reichstein
经典的Cayley映射X ->（I_n-X）/（I_n+X）是特殊正交群SO_n与其李代数SO_n之间的双有理同构，SO_n分别关于共轭作用和伴随作用是SO_n-等变的。我们问是否可以为其他代数群构造具有这些性质的映射。我们表明，答案通常是“不”，有几个例外。特别地，我们证明了SL_n的Cayley映射存在的充要条件是n<= 3.这回答了一个关于月亮的老问题。
The classical Cayley map, X -->(I_n-X)/(I_n+X), is a birational isomorphism between the special orthogonal group SO_n and its Lie algebra so_n, which is SO_n-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 SL_n exists if and only if n<= 3. This answers an old question of Luna.